- "Phase structure and vortex configurations of superconductors coexisting with ferromagnetism",

Hidetoshi Ozawa, Akihiro Shimizu, Ikuo Ichinose, and Tetsuo Matsui

doi:10.1088/1742-6596/400/2/022095

J. Phys.: Conf. Ser. 400 (2012) 022095- Abstract - We study the Ginzburg-Landau lattice gauge model that we introduced recently for ferromagnetic superconductors, i.e., superconductors in which the p-wave superconducting (SC) order and the ferromagnetic (FM) order may coexist. We report some interesting results obtained by Monte-Carlo simulations. In particular, we have two types of coexisting states distinguished by the transition temperatures of the SC order TSC and the FM order TFM; (i) homogeneous state for TFM/TSC > 1 and (ii) inhomogeneous state for TFM/TSC < 0.7. In (ii) the two orders appear only near the surface of the lattice as observed in ZrZn2. We also study vortex configurations of SC order parameters. Two kinds of vortices, one for spin-up electron pairs and one for spin-down pairs show different behaviors because of the Zeeman coupling.

- "Dynamical properties of bosons in an optical lattice with a synthetic magnetic field",

Kenichi Kasamatsu, Akira Kato, Yuki Nakano, and Tetsuo Matsui

doi:10.1088/1742-6596/400/1/012026

J. Phys.: Conf. Ser. 400 (2012) 012026- Abstract - We study the dynamical properties of bosons in an optical lattice subject to a synthetic magnetic field at zero temperature. First, we consider a superfluid regime where the nearest-neighbor hopping is much larger than the on-site repulsion and a large number of bosons are occupied in each site. Then, the dynamics is well described by the discrete nonlinear Schroedinger equation. Second, we study the dynamics of hard-core bosons as a limit of the strong interparticle interaction by solving the truncated Green's functions for the boson and density operators. We discuss the evolution of the density and the vorticity, which are clearly distinct between two regimes.

- "The t-J model of hard-core bosons in slave-particle representation and its Monte-Carlo simulations",

Yuki Nakano, Takumi Ishima, Naohiro Kobayashi, Kazuhiko Sakakibara, Ikuo Ichinose, and Tetsuo Matsui

doi:10.1088/1742-6596/400/3/032064

J. Phys.: Conf. Ser. 400 (2012) 032064- Abstract - We study the system of hard-core bosons (HCB) with two species in the three-dimensional lattice at finite temperatures. In the strong-correlation limit, the system becomes the bosonic t-J model, that is, the t-J model of "bosonic electrons". The bosonic "electron" operator Bx at the site x with a two-component spin (= 1, 2***) is treated as a HCB operator, and represented by a composite of two slave particles; a spinon described by a Schwinger boson (CP1 boson) zx and a holon described by a HCB field x as Bx = xzx.*** This x is again represented by another CP1 quasi-spinon operator xa*** (a = 1, 2***). The phase diagrams of the resulting double CP1 system obtained by Monte Carlo simulations involve first-order and second-order phase boundaries. We present in detail the techniques and algorithm to reduce the hysteresis and locate the first-order transition points.

- "Z(2) Gauge Neural Network and its Phase Structure",

Yusuke Takafuji, Yuki Nakano, and Tetsuo Matsui

arXiv:1206.1110 DOI: 10.1016/j.physa.2012.06.009

Physica A 391 (2012) 5258-5304.- Abstract - We study general phase structures of neural-network models that have Z(2) local gauge symmetry. The Z(2) spin variable Si = \pm1 on the i-th site describes a neuron state as in the Hopfield model, and the Z(2) gauge variable Jij = \pm1 describes a state of the synaptic connection between j-th and i-th neurons. The gauge symmetry allows for a self-coupling energy among Jij's such as JijJjkJki, which describes reverberation of signals. Explicitly, we consider the three models; (I) annealed model with full and partial connections of Jij, (II) quenched model with full connections where Jij is treated as a slow quenched variable, and (III) quenched three-dimensional lattice model with the nearest-neighbor connections. By numerical simulations, we examine their phase structures paying attention to the effect of reverberation term, and compare them each other and with the annealed 3D lattice model which has been studied beforehand. By noting the dependence of thermodynamic quantities upon the total number of sites and the connectivity among sites, we obtain a coherent interpretation to understand these results. Among other things, we find that the Higgs phase of the annealed model is separated into two stable spin-glass phases in the quenched cases (II) and (III).

- "Lattice Ginzburg-Landau model of a ferromagnetic p-wave pairing phase in superconducting materials and an inhomogeneous coexisting state",

Akihiro Shimizu, Hidetoshi Ozawa, and Ikuo Ichinose, and Tetsuo Matsui

arXiv:1106.3130 DOI: 10.1103/PhysRevB.85.144524

Physical Review B 85 (2012) 144524 (1-9).- Abstract - We study the interplay of the ferromagnetic (FM) state and the p-wave superconducting (SC) state observed in several materials such as UCoGe and URhGe in a totally nonperturbative manner. To this end, we introduce a lattice Ginzburg-Landau model that is a genuine generalization of the phenomenological Ginzburg-Landau theory proposed previously in the continuum and also a counterpart of the lattice gauge Higgs model for the s-wave SC transition, and study it numerically by Monte Carlo simulations. The obtained phase diagram has qualitatively the same structure as that of UCoGe in the region where the two transition temperatures satisfy TFM>TSC. For TFM/TSC<0.7, we find that the coexisting region of FM and SC orders appears only near the surface of the lattice, which describes an inhomogeneous FMSC coexisting state.

- "Finite-temperature phase structures of hard-core bosons in an optical lattice with an
effective magnetic field",

Yuki Nakano, Kenichi Kasamatsu, and Tetsuo Matsui

arXiv:1112.0145 DOI: 10.1103/PhysRevA.85.023622

Physical Review A 85 (2012) 023622 (1-11).- Abstract - We study finite-temperature phase structures of hard-core bosons in a two-dimensional optical lattice subject to an effective magnetic field by employing the gauged CP1 model. Based on the extensive Monte Carlo simulations, we study their phase structures at finite temperatures for several values of the magnetic flux per plaquette of the lattice and mean particle density. Despite the presence of the particle number fluctuation, the thermodynamic properties are qualitatively similar to those of the frustrated XY model with only the phase as a dynamical variable. This suggests that cold atom simulators of the frustrated XY model are available irrespective of the particle filling at each site.

- "Finite-temperature phase diagram of two-component bosons in a cubic optical lattice: Three-dimensional t-J model of hard-core bosons",

Yuki Nakano, Takumi Ishima, Naohiro Kobayashi, Takahiro Yamamoto, Ikuo Ichinose, and Tetsuo Matsui

arXiv:1111.1537 DOI: 10.1103/PhysRevA.85.023617

Physical Review A 85 (2012) 023617 (1-10).- Abstract - We study the three-dimensional bosonic t-J model, i.e., the t-J model of "bosonic electrons", at finite temperatures. This model describes the s=1/2 Heisenberg spin model with the anisotropic exchange coupling J_{\bot}=-\alpha J_z and doped bosonic holes, which is an effective system of the Bose-Hubbard model with strong repulsions. The bosonic "electron" operator B_{r\sigma} at the site r with a two-component (pseudo-)spin \sigma (=1,2) is treated as a hard-core boson operator, and represented by a composite of two slave particles; a "spinon" described by a Schwinger boson (CP^1 boson) z_{r\sigma} and a "holon" described by a hard-core-boson field \phi_r as B_{r\sigma}=\phi^\dag_r z_{r\sigma}. By means of Monte Carlo simulations, we study its finite-temperature phase structure including the \alpha dependence, the possible phenomena like appearance of checkerboard long-range order, super-counterflow, superfluid, and phase separation, etc. The obtained results may be taken as predictions about experiments of two-component cold bosonic atoms in the cubic optical lattice.

- "Vortex formation of a Bose-Einstein condensate in a rotating deep optical lattice",

Akira Kato, Yuki Nakano, Kenichi Kasamatsu, and Tetsuo Matsui

arXiv:1108.1857 DOI: 10.1103/PhysRevA.84.053623

Physical Review A 84 (2011) 053623 (1-7).- Abstract - We study the dynamics of vortex nucleation and lattice formation in a Bose-Einstein condensate in a rotating square optical lattice by numerical simulations of the Gross-Pitaevskii equation. Different dynamical regimes of vortex nucleation are found, depending on the depth and period of the optical lattice. We make an extensive comparison with the experiments by Williams et al. [Phys. Rev. Lett. 104, 050404 (2010)], especially focusing on the issues of the critical rotation frequency for the first vortex nucleation and the vortex number as a function of rotation frequency.

- "Finite-temperature phase diagram of the three-dimensional hard-corebosonic t-J model",

Yuki Nakano, Takumi Ishima, Naohiro Kobayashi, Kazuhiko Sakakibara, Ikuo Ichinose, Tetsuo Matsui

arXiv:1005.3997 DOI: 10.1103/PhysRevB.83.235116

Physical Review B 83 (2011) 235116 (1-15).- Abstract - We study the three-dimensional bosonic t-J model, i.e., the t-J model of ``bosonic electrons" at finite temperatures. This model describes a system of isotropic antiferromagnet with doped bosonic holes, and is closely related to systems of two-component bosons in an optical lattice. The bosonic ``electron" operator B_{x\sigma} at the site x with a two-component spin \sigma (=1,2) is treated as a hard-core boson operator, and represented by a composite of two slave particles; a spinon described by a Schwinger boson (CP^1 boson) z_{x\sigma} and a holon described by a hard-core-boson field \phi_x as B_{x\sigma}=\phi^\dag_x z_{x\sigma}. By means of Monte Carlo simulations of this bosonic t-J model, we study its phase structure and the possible phenomena like appearance of antiferromagnetic long-range order, Bose-Einstein condensation, phase separation, etc. Obtained results show that the bosonic t-J model has a phase diagram that suggests some interesting implications for high-temperature superconducting materials.

- "Antiferromagnetic, metal-insulator, and superconducting phase transitions in underdoped cuprates: Slave-fermion t-J model in the hopping expansion",

Akihiro Shimizu, Koji Aoki, Kazuhiko Sakakibara, Ikuo Ichinose, and Tetsuo Matsui

arXiv:1007.4273 DOI: 10.1103/PhysRevB.83.064502

Physical Review B 83 (2011) 064502 (1-15).- Abstract - We study a system of doped antiferromagnet in three dimensions at finite temperatures using the t -J model, a canonical model of strongly correlated electrons. We employ the slave-fermion representation of electrons, in which an electron is described as a composite of a charged spinless holon and a chargeless spinon. We introduce two kinds of U(1) gauge fields on links as auxiliary fields, one describing resonating valence bonds of antiferromagnetic nearest-neighbor spin pairs and the other for nearest-neighbor hopping amplitudes of holons and spinons in the ferromagnetic channel. To perform a numerical study of the system, we integrate out the fermionic holon field by using the hopping expansion in powers of the hopping amplitude, which is legitimate for the region in and near the insulating phase. The resultant effective model is described in terms of bosonic spinons, two U(1) gauge fields, and a collective field for hole pairs. We study this model by means of Monte Carlo simulations, calculating the specific heat, spin correlation functions, and instanton densities. We obtain a phase diagram in the hole concentration-temperature plane, which is in good agreement with that observed recently for clean and homogeneous underdoped samples.

- "Random Z(2) Higgs Lattice Gauge Theory in Three Dimensions and
its Phase Structure",

Shunsuke Doi, Ryosuke Hamano, Teppei Kakisako, Keiko Takada, Tetsuo Matsui

arXiv:0902.0142- Abstract - We study the three-dimensional random Z(2) lattice gauge theory with Higgs field, which has the link Higgs coupling $c_1 SUS$ and the plaquette gauge coupling $c_2 UUUU$. The randomness is introduced by replacing $c_1 \to -c_1$ for each link with the probability $p_1$ and $c_2 \to -c_2$ for each plaquette with the probability $p_2$. We calculate the phase diagram by a new kind of mean field theory that does not assume the replica symmetry and also by Monte Carlo simulations. For the case $p_1=p_2(\equiv p)$, the Monte Carlo simulations exhibit that (i) the region of the Higgs phase in the Coulomb-Higgs transition diminishes as $p$ increases, and (ii) the first-order phase transition between the Higgs and the confinement phases disappear for $p \ge p_c \simeq 0.01$. We discuss the implications of the results to the quantum memory studied by Kitaev et al. and the Z(2) gauge neural network on a lattice.

- "Effects of Disorder on a Lattice Ginzburg-Landau Model
of d-wave Superconductors and Superfluids",

Tomonori Shimizu, Shunsuke Doi, Ikuo Ichinose, Tetsuo Matsui

arXiv:0812.4645 DOI: 10.1103/PhysRevB.79.092508

Physical Review B 79 (2009) 092508 (1-4).- Abstract - We study the effects of quenched disorder on the two-dimensional $d$-wave superconductors (SC's) at zero temperature by Monte-Carlo simulations. The model is defined on the three-dimesional (3D) lattice and the SC pair field is put on each spatial link as motivated in the resonating-valence-bond theory of the high-$T_{\rm c}$ SC's. For the nonrandom case, the model exhibits a second-order phase transition to a SC state as density of charge carriers is increased. It belongs to the universality class {\it different from} that of the 3D XY model. Quenched disorders (impurities) are introduced both in the hopping amplitude and the plaquette term of pair fields. Then the second-order transition disappears at a critical concentration of quenched disorder, $p_c\simeq 15\%$. Implication of the results to cold atomic systems in optical lattices is also discussed.

- "Magnetic Order, Bose-Einstein Condensation, and Superfluidity in a Bosonic
t-J Model of CP$^1$ Spinons and Doped Higgs Holons",

Koji Aoki, Kazuhiko Sakakibara, Ikuo Ichinose, Tetsuo Matsui

arxiv.org:0811.2845 DOI: 10.1103/PhysRevB.80.144510

Physical Review B 80 (2009) 144510 (1-12)- Abstract - We study the three-dimensional U(1) lattice gauge theory of a CP1 spinon (Schwinger boson) field and a Higgs field. It is a bosonic t-J model in slave-particle representation, describing the antiferromagnetic (AF) Heisenberg spin model with doped bosonic holes expressed by the Higgs field. The spinon coupling term of the action favors AF long-range order, whereas the holon hopping term in the ferromagnetic channel favors Bose-Einstein condensation (BEC) of holons. We investigate the phase structure by means of Monte Carlo simulations and study an interplay of AF order and BEC of holes. We consider the two variations in the model; (i) the three-dimensional model at finite temperatures, and (ii) the two-dimensional model at vanishing temperature. In the model (i) we find that the AF order and BEC coexist at low temperatures and certain hole concentrations. In the model (ii), by varying the hole concentration and the stiffness of AF spin coupling, we find a phase diagram similar to the model (i). Implications of the results to systems of cold atoms and the fermionic t-J model of strongly correlated electrons are discussed.

- "Four-dimensional CP$^1+$ U(1) lattice gauge theory
for 3D antiferromagnets:

Phase structure, gauge bosons and spin liquid",

Kenji Sawamura, Takashi Hiramatsu, Katsuhiro Ozaki, Ikuo Ichinose, Tetsuo Matsui

arXiv:0711.0818 DO: 10.1103/PhysRevB.77.224404

Physical Review B 77 (2008) 224404 (1-4).- Abstract - In this paper we study the lattice CP$^1$ model in ($3+1$) dimensions coupled with a dynamical compact U(1) gauge field. This model is an effective field theory of the $s={1 \over 2}$ antiferromagnetic Heisenberg spin model in three spatial dimensions. By means of Monte Carlo simulations, we investigate its phase structure. There exist the Higgs, Coulomb and confinement phases, and the parameter regions of these phases are clarified. We also measure magnetization of O(3) spins, energy gap of spin excitations, and mass of gauge boson. Then we discuss the relationship between these three phases and magnetic properties of the high-$T_{\rm c}$ cuprates, in particular the possibility of deconfined-spinon phase. Effect of dimer-like spin exchange coupling and ring-exchange coupling is also studied.

- "Phase structure and critical behavior of multi-Higgs U(1) lattice gauge theory in three dimensions",

Tomoyoshi Ono, Shunsuke Doi, Yuki Hori, Ikuo Ichinose, and Tetsuo Matsui,

arXiv:0712.2291 doi:10.1016/j.aop.2009.09.002

Annals of Physics 324 (2009) 2453-2464.- Abstract - We study the three-dimensional (3D) compact U(1) lattice gauge theory coupled with $N$-flavor Higgs fields by means of the Monte Carlo simulations. This model is relevant to multi-component superconductors, antiferromagnetic spin systems in easy plane, inflational cosmology, etc. It is known that there is no phase transition in the $N=1$ model. For $N=2$, we found that the system has a second-order phase transition line $\tilde{c}_1(c_2)$ in the $c_2$(gauge coupling)$-c_1$(Higgs coupling) plane, which separates the confinement phase and the Higgs phase. Numerical results suggest that the phase transition belongs to the universality class of the 3D XY model as the previous works by Babaev et al. and Smiseth et al. suggested. For $N=3$, we found that there exists a critical line similar to that in the $N=2$ model, but the critical line is separated into two parts; one for $c_2 < c_{2{\rm tc}}=2.4\pm 0.1$ with first-order transitions, and the other for $ c_{2{\rm tc}} < c_2$ with second-order transitions, indicating the existence of a tricritical point. We verified that similar phase diagram appears for the $N=4$ and $N=5$ systems. We also studied the case of anistropic Higgs coupling in the $N=3$ model and found that there appear two second-order phase transitions or a single second-order transition and a crossover depending on the values of the anisotropic Higgs couplings. This result indicates that an ``enhancement" of phase transition occurs when multiple phase transitions coincide at a certain point in the parameter space.

- "Phase structure of a U(1) lattice gauge
theory with dual gauge fields",

Tomoyoshi Ono, Yuki Moribe, Shunsuke Takashima, Ikuo Ichinose, Tetsuo Matsui, and Kazuhiko Sakakibara,

cond-mat/0606079

Nuclear Physics B 764 [FS] (2007) 168-182.- Abstract - We introduce a U(1) lattice gauge theory with dual gauge fields and study its phase structure. This system is partly motivated by unconventional superconductors like extended $s$-wave and $d$-wave superconductors in the strongly-correlated electron systems and also studies of the $t-J$ model in the slave-particle representation. In this theory, the ``Cooper-pair" (or RVB spinon-pair) field is put on links of a cubic lattice due to strong on-site repulsion between original electrons in contrast to the ordinary $s$-wave pair field on sites. This pair field behaves as a gauge field dual to the U(1) gauge field coupled with the hopping of electrons or quasi-particles of the $t-J$ model, holons and spinons. By Monte Carlo simulations we study this lattice gauge model and find a first-order phase transition from the normal state to the Higgs (superconducting) phase. Each gauge field works as a Higgs field for the other gauge field. This mechanism requires no scalar fields in contrast to the ordinary Higgs mechanism. An explicit microscopic model is introduced, the low-energy effective theory of which is viewed as a special case of the present model.

- "Self-Reduction Rate of a Microtubule",

Takashi Hiramatsu, Tetsuo Matsui, and Kazuhiko Sakakibara

quant-ph/0602144

International Journal of Modern Physics C 19 (2008) 291-305.- Abstract - We formulate and study a quantum field theory of a microtubule, a basic element of living cells. Following the quantum theory of consciousness by Hameroff and Penrose, we let the system to reduce to one of the classical states without measurement if certain conditions are satisfied(self-reductions), and calculate the self-reduction time \tau_N (the mean interval between two successive self-reductions) of a cluster consisting of more than N neighboring tubulins (basic units composing a microtubule). \tau_N is interpreted there as an instance of the stream of consciousness. We analyze the dependence of \tau_N upon N and the initial conditions, etc. For relatively large electron hopping amplitude, \tau_N obeys a power law \tau_N \sim N^b, which can be explained by the percolation theory. For sufficiently small values of the electron hopping amplitude, \tau_N obeys an exponential law, \tau_N \sim \exp(c' N). By using this law, we estimate the condition for \tau_N to take realistic values \tau_N >\sim 10^{-1} sec as N >\sim 1000.

- "Deconfinement of Spinons on Critical Points: Multi-Flavor CP^1 + U(1) Lattice Gauge Theory in Three Dimensions",

Shunsuke Takashima, Ikuo Ichinose, Tetsuo Matsui

cond-mat/0511107

Physical Review B 73 (2006) 075119 (1-7).- Abstract - In this paper, we study the 3D $N_{\rm f}$-flavor CP$^1$ model (a set of $N_{\rm f}$ CP$^1$ variables) coupled with a dynamical compact U(1) gauge field by means of Monte-Carlo simulations. This model is relevant to 2D $s=1/2$ quantum spin models, and has a phase transition line which separates an ordered phase of global spin symmetry from a disordered one. From gauge theoretical point of view, the ordered phase is a Higgs phase whereas the disordered phase is a confinement phase. We are interested in the gauge dynamics just on the critical line, in particular, whether a Coulomb-like deconfinement phase is realized there. This problem is quite important to clarify low-energy excitations in certain class of quantum spin models. If the gauge dynamics is in the deconfinement phase there, spinons, which transform in the fundamental representation of the SU($N_{\rm f}$) symmetry, appear as low-energy excitations. By Monte-Carlo simulations, we found that the "phase structure" on the {\em criticality} strongly depends on the value of $N_{\rm f}$. For small $N_{\rm f}$, the confinement phase is realized, whereas the deconfinement phase appears for sufficient large $N_{\rm f}\ge 14$. This result strongly suggests that compact QED$_3$ is in a deconfinement phase for sufficiently large number of flavors of massless fermions.

- "Three Phases in the Three-Dimensional Abelian Higgs Model with Nonlocal Gauge Interactions",

Shunsuke Takashima, Ikuo Ichinose, Tetsuo Matsui, Kazuhiko Sakakibara

hep-lat/0511010

Physical Review B 74 (2006) 075111 (1-6).- Abstract - We study the phase structure of the three-dimensional (3D) nonlocal compact U(1) lattice gauge theory coupled with a Higgs field by Monte Carlo simulations. The nonlocal interactions among gauge variables are along the temporal direction and mimic the effect of local coupling to massless particles. In contrast to the 3D local abelian Higgs model having only the confinement phase, the present model exhibits the confinement, Higgs, and Coulomb phases separated by three second-order transition lines emanating from a triple point. This result is relevant not only to the 3D massless QED coupled with a Higgs field but also to electron fractionalization phenomena in strongly-correlated electron systems like the high-$T_c$ superconductors and the fractional quantum Hall effect.

- "Phase Structure of a 3D Nonlocal U(1) Gauge Theory: Deconfinement by Gapless Matter Fields",

Gaku Arakawa, Ikuo Ichinose, Tetsuo Matsui, Kazuhiko Sakakibara, Shunsuke Takashima

cond-mat/0506529

Nuclear Physics B 732 (2006) 401-425.

- Abstract - In this paper, we study a 3D compact U(1) lattice gauge theory with a variety of nonlocal interactions that simulates the effects of gapless/gapful matter fields. This theory is quite important to investigate the phase structures of QED$_3$ and strongly-correlated electron systems like the 2D quantum spin models, the fractional quantum Hall effect, the t-J model of high-temperature superconductivity. We restrict the nonlocal interactions among gauge variables only to those along the temporal direction and adjust their coupling constants optimally to simulate the isotropic nonlocal couplings of the original models. We perform numerical studies of the model to find that, for a certain class of power-decaying couplings, there appears a second-order phase transition to the deconfinement phase as the gauge coupling constant is decreased. On the other hand, for the exponentially-decaying coupling, there are no signals for second-order phase transition. These results indicate the possibility that introduction of sufficient number of massless matter fields destabilizes the permanent confinement in the 3D compact U(1) pure gauge theory due to instantons.

- "CP^1+ U(1) Lattice Gauge Theory in Three Dimensions:
Phase Structure, Spins, Gauge Bosons, and Instantons",

Shunsuke Takashima, Ikuo Ichinose, Tetsuo Matsui

cond-mat/0504193

Physical Review B 72 (2005) 075112 (1-16).

- Abstract - In this paper we study a 3D lattice spin model of CP$^1$ Schwinger-bosons coupled with dynamical compact U(1) gauge bosons. The model contains two parameters; the gauge coupling and the hopping parameter of CP$^1$ bosons. At large (weak) gauge couplings, the model reduces to the classical O(3) (O(4)) spin model with long-range and/or multi-spin interactions. It is also closely related to the recently proposed ``Ginzburg-Landau" theory for quantum phase transitions of $s=1/2$ quantum spin systems in a 2D plane at zero temperature. We numerically study the phase structure of the model by calculating specific heat, spin correlations, instanton density, and gauge-boson mass. The model has two phases separated by a critical line of second-order phase transition; O(3) spin-ordered phase and the spin-disordered phase. The spin-ordered phase is the Higgs phase of U(1) gauge dynamics, whereas the disordered phase is the confinement phase. %We observe how the %instanton density changes near the critical line. We find a crossover in the confinement phase which separates dense and dilute regions of instantons. On the critical line, spin excitations are gapless, but the gauge-boson mass is {\it nonvanishing}. This indicates that a confinement phase is realized on the critical line. To confirm this point, we also study the noncompact version of the model. A possible realization of a deconfinement phase on the criticality is discussed for the CP$^N$+U(1) model with larger $N$.

- "Deconfinement Phase Transition in a 3D Nonlocal U(1) Lattice Gauge Theory",

Gaku Arakawa, Ikuo Ichinose, Tetsuo Matsui, Kazuhiko Sakakibara

hep-th/0502013

Physical Review Letters, 94 (2005) 211601.

- Abstract - We introduce a 3D compact U(1) lattice gauge theory having nonlocal interactions in the temporal direction, and study its phase structure. The model is relevant for the compact QED$_3$ and strongly correlated electron systems like the t-J model of cuprates. For a power-law decaying long-range interaction, which simulates the effect of gapless matter fields, a second-order phase transition takes place separating the confinement and deconfinement phases. For an exponentially decaying interaction simulating gapfull matter fields, the system exhibits no signals of a second-order transition.

- "Self-Duality and Phase Structure of the 4D Random-Plaquette Z_2 Gauge Model",

Gaku Arakawa, Ikuo Ichinose, Tetsuo Matsui, Koujin Takeda

hep-th/0409076 Nuclear Physics B 709 (2005) 296-306.

- Abstract - In the present paper, we shall study the 4-dimensional Z_2 lattice gauge model with a random gauge coupling; the random-plaquette gauge model(RPGM). The random gauge coupling at each plaquette takes the value J with the probability 1-p and -J with p. This model exhibits a confinement-Higgs phase transition. We numerically obtain a phase boundary curve in the (p-T)-plane where T is the "temperature" measured in unit of J/k_B. This model plays an important role in estimating the accuracy threshold of a quantum memory of a toric code. In this paper, we are mainly interested in its "self-duality" aspect, and the relationship with the random-bond Ising model(RBIM) in 2-dimensions. The "self-duality" argument can be applied both for RPGM and RBIM, giving the same duality equations, hence predicting the same phase boundary. The phase boundary curve obtained by our numerical simulation almost coincides with this predicted phase boundary at the high-temperature region. The phase transition is of first order for relatively small values of p < 0.08, but becomes of second order for larger p. The value of p at the intersection of the phase boundary curve and the Nishimori line is regarded as the accuracy threshold of errors in a toric quantum memory. It is estimated as p=0.110\pm0.002, which is very close to the value conjectured by Takeda and Nishimori through the "self-duality" argument.

- "Neel-Dimer Transition in Antiferromagnetic Heisenberg model and Deconfinement of Spinons at the Critical Point",

Daisuke Yoshioka, Gaku Arakawa, Ikuo Ichinose, Tetsuo Matsui

cond-mat/0404427

Physical Review B 70 (2004) 174407(1-4)

- Abstract - Quantum phase transition from the N\'eel to the dimer states in an antiferromagnetic(AF) Heisenberg model on square lattice is studied. We introduce a control parameter $\alpha$ for the exchange coupling which connects the N\'eel ($\alpha=0$) and the dimer ($\alpha=1$) states. We employ the $CP^1$ (the Schwinger boson) representation of the $s={1\over 2}$ spin operator and integrate out the half of the $CP^1$ variables at odd sites and we obtain a $CP^1$ nonlinear $\sigma$ model. The effective coupling constant is a function of $\alpha$ and at $\alpha=0$ the $CP^1$ model is in the ordered phase which corresponds to the N\'eel state of the AF Heisenberg model. A phase transition to the dimer state occurs at a certain critical value of $\alpha_C$ as $\alpha$ increases. In the N\'eel state, the dynamical composite U(1) gauge field in the $CP^1$ model is in a Higgs phase and low-energy excitations are gapless spin wave. In the dimer phase, a confinement phase of the gauge theory is realized and low-energy excitations are $s=1$ magnons. For the critical point, we argue that a deconfinement phase, which is similar to the Coulomb phase in 3 spatial dimensions, is realized and $s={1\over 2}$ spinons appear as low-energy excitations.

- "Phase Structure of the Random-Plaquette Z_2 Gauge Model: Accuracy Threshold for a Toric Quantum Memory",

Takuya Ohno, Gaku Arakawa, Ikuo Ichinose, Tetsuo Matsui

quant-ph/0401101

Nuclear Physics B 697 (2004) 462-480.

- Abstract - We study the phase structure of the random-plaquette Z_2 lattice gauge model in three dimensions. In this model, the "gauge coupling" for each plaquette is a quenched random variable that takes the value \beta with the probability 1-p and -\beta with the probability p. This model is relevant for the recently proposed quantum memory of toric code. The parameter p is the concentration of the plaquettes with "wrong-sign" couplings -\beta, and interpreted as the error probability per qubit in quantum code. In the gauge system with p=0, i.e., with the uniform gauge couplings \beta, it is known that there exists a second-order phase transition at a certain critical "temperature", T(\equiv \beta^{-1}) = T_c =1.31, which separates an ordered(Higgs) phase at T

T_c. As p increases, the critical temperature T_c(p) decreases. In the p-T plane, the curve T_c(p) intersects with the Nishimori line T_{N}(p) at the certain point (p_c, T_{N}(p_c)). The value p_c is just the accuracy threshold for a fault-tolerant quantum memory and associated quantum computations. By the Monte-Carlo simulations, we calculate the specific heat and the expectation values of the Wilson loop to obtain the phase-transition line T_c(p) numerically. The accuracy threshold is estimated as p_c \simeq 0.033.

- "Gauge Theory of Composite Fermions:
Particle-Flux Separation in Quantum Hall Systems",

I.Ichinose and T.Matsui

cond-mat/0210142

Physical Review B 68 (2003) 085322(1-19).

- Abstract - Fractionalization phenomenon of electrons in quantum Hall states is studied in terms of U(1) gauge theory. We focus on the Chern-Simons(CS) fermion description of the quantum Hall effect(QHE) at the filling factor $\nu=p/(2pq\pm 1)$, and show that the successful composite-fermions(CF) theory of Jain acquires a solid theoretical basis, which we call particle-flux separation(PFS). PFS is studied efficiently by a gauge theory and characterized as a deconfinement phenomenon in the corresponding gauge dynamics. The PFS takes place at low temperatures, $T \leq T_{\rm PFS}$, where each electron or CS fermion splinters off into two quasiparticles, a fermionic chargeon and a bosonic fluxon. The chargeon is nothing but Jain's CF, and the fluxon carries $2q$ units of CS fluxes. At sufficiently low temperatures $T \leq T_{\rm BC} ( < T_{\rm PFS})$, fluxons Bose-condense uniformly and (partly) cancel the external magnetic field, producing the correlation holes. This partial cancellation validates the mean-field theory in Jain's CF approach. FQHE takes place at $T < T_{\rm BC}$ as a joint effect of (i) integer QHE of chargeons under the residual field $\Delta B$ and (ii) Bose condensation of fluxons. We calculate the transition temperature $T_{\rm PFS}$ and the CF mass. Repulsive interactions between electrons are essential to establish PFS. PFS is a counterpart of the charge-spin separation in the t-J model of high-$T_{\rm c}$ cuprates in which each electron dissociates into holon and spinon. Quasiexcitations and resistivity in the PFS state are also studied. The resistivity is just the sum of contributions of chargeons and fluxons, and we conjecture that $\rho_{xx}$ acquires extra reduction factor below $T_{\rm PFS}$ from the expected $T$-linear behavior.

- "Quantum Gauged Neural Network: U(1) Gauge Theory",

Y.Fujita and T.Matsui

cond-mat/0207023

Proceedings of 9th International Conference on Neural Information Processing, ed. by L.Wang et al. (2002)1360-1367.

- Abstract - A quantum model of neural network is introduced and studied. The model is an extension of the classical Z(2) gauged neural network of learning and recalling to a quantum model by replacing the Z(2) variables $S_i = \pm1$ of neurons and $J_{ij} =\pm1$ of synaptic connections to U(1) phase variables $S_i = \exp(i\varphi_i)$ and $J_{ij} = \exp(i\theta_{ij}) $ which describe the phase parts of the wave functions (local order parameters) of each neuron and synaptic connection. The model takes the form similar to the abelian Higgs lattice gauge theory and the Ginzburg-Landau theory of superconductivity. Its current may describe the flow of chemical materials transfered via synaptic connections. The phase structure of the model at finite temperatures is examined by the mean-field theory, and Coulomb, Higgs and confinement phases are obtained. By comparing with the result of the $Z(2)$ model, the quantum effects is shown to weaken the ability of learning and recalling.

- "Gauge Theory of Composite Fermions",

I.Ichinose and T.Matsui

Physica E 18 (2003) 132-133.

- Abstract - We explain the success of Jain's composite fermion theory for quantum Hall systems at the filling factor \nu =p/(2pq}1) by applying the gauge theory of particle-flux separation. At temperaturesT < T_{PFS}(\nu) (\simeq 5.7 \sim 6.7 K for \nu=1/2), the charge and Chern?Simons flux degrees of freedom of electrons separate. We call quasiparticles carrying each quantum number chargeons and fluxons, respectively. Bose condensation of fluxons below T_{BC} (< T_{PFS}) justifies the (partial) cancellation of the external magnetic field, as assumed in the composite-fermion theory. The resistivity \rho_{xx} acquires an extra reduction factor below T_{PFS} from the expected T-linear behavior.

- "Gauged Neural Network: Phase Structure, Learning, and Associative
Memory",

M.Kemuriyama, K.Sakakibara and T.Matsui

cond-mat/0203136

Physica A 356 (2005) 525-553.- Abstract - A gauge model of neural network is introduced, which resembles Z(2) Higgs lattice gauge theory of high-energy physics. It contains a neuron variable $S_x = \pm 1$ on each site $x$ of a 3D lattice and a synaptic-connection variable $J_{x\mu} = \pm 1$ on each link $(x,x+\hat{\mu}) (\mu=1,2,3)$. The model is regarded as a generalization of the Hopfield model of associative memory to a model of learning by converting the synaptic weight between $x$ and $x+\hat{\mu}$ to a dynamical Z(2) gauge variable $J_{x\mu}$. The local Z(2) gauge symmetry is inherited from the Hopfield model and assures us the locality of time evolutions of $S_x$ and $J_{x\mu}$ and a generalized Hebbian learning rule. At finite ``temperatures", numerical simulations show that the model exhibits the Higgs, confinement, and Coulomb phases. We simulate dynamical processes of learning a pattern of $S_x$ and recalling it, and classify the parameter space according to the performance. At some parameter regions, stable column-layer structures in signal propagations are spontaneously generated. Mutual interactions between $S_x$ and $J_{x\mu}$ induce partial memory loss as expected.

- "Particle-Flux Separation and Quasiexcitations in Quantum Hall Systems",

I.Ichinose and T.Matsui

cond-mat/0202030

Journal of the Physical Society of Japan, Letters,**71**(2002) 1828-1831.- Abstract - The quasiexcitations of quantum Hall systems at the filling factor $\nu = p/(2pq \pm 1)$ are studied in terms of chargeon and fluxon introduced previously as constituents of an electron at $\nu = 1/2$. At temperatures $T < T_{\rm PFS}(\nu)$, the phenomenon so-called particle-flux separation takes place, and chargeons and fluxons are deconfined to behave as quasiparticles. Bose condensation of fluxons justify the (partial) cancellation of external magnetic field. Fluxons describe correlation holes, while chargeons describe composite fermions. They contribute to the resistivity $\rho_{xy} = h/(\nu e^2)$ additively.

- "Effects of External Stimuli on a Neural Network",

S.Tatsumi and T.Matsui

Journal of the School of Science and Engineering, Kinki University**37**(2001) 9-14.- Abstract - A new model of neural network of the Hopfield type is proposed, which simulates the effects of external stimuli upon a neural network. The model consists of two parts; the internal part is a neural network to exhibit associated memory, and the external part is a collection of neurons transmitting external stimuli to the internal network. When the external part is set to a particular configuration that correponds to one of the pattern to memorize in the internal part, the energy minimum around that pattern becomes lower and help to recall it.

- "Gauge-Theoretical Study of the t-J Model: (De)Confinement and the Charge-Spin
Separation" (in Japanese),

I.Ichinose and T.Matsui

"Butsrui Gakkaishi", the Bulletin of the Physical Society of Japan,**56**(2001) 604-608.- Abstract - We present a review of gauge-theoretical study of the t-J model, mainly based on our studies on the charge-spin separation of strongly-correlated electrons as a deconfinement phenomenon of the gauge dunamics of the effective gauge theory.

- "Effective Gauge Field Theory of the
t-J Model in the Charge-Spin Separated State and its Transport Properties",

I.Ichinose, T.Matsui and M.Onoda

cond-mat/0103007

Physical Review B 64 (2001) 104516(1-22).- Abstract - We study the slave-boson t-J model of cuprates with high superconducting transition temperatures, and derive its low-energy effective field theory for the charge-spin separated state in a self-consistent manner. The phase degrees of freedom of the mean field for hoppings of holons and spinons can be regarded as a U(1) gauge field, A

_{i}. The charge-spin separation occurs below certain temperature, T_{CSS}, as a deconfinement phenomenon of the dynamics of A_{i}. Below certain temperature T_{SG}( < T_{CSS}), the spin-gap phase develops as the Higgs phase of the gauge-field dynamics, and A_{i}acquires a mass m_{A}. The effective field theory near T_{SG}takes the form of Ginzburg-Landau theory of a complex scalar field coupled with A_{i}, where represents d-wave pairings of spinons. Three dimensionality of the system is crucial to realize a phase transition at T_{SG}. By using this field theory, we calculate the dc resistivity . At T > T_{SG}, is proportional to T. At T < T_{SG}, it deviates downward from the T-linear behavior as T [ 1 - c (T_{SG}- T )^{d}]. When the system is near (but not) two dimensional, due to the compactness of the phase of the field $\lambda$, the exponent d deviates from its mean-field value 1/2 and becomes a nonuniversal quantity which depends on temperature and doping. This significantly improves the comparison with the experimental data.

- Comment on "Confinement of Slave Particles
in U(1) Gauge Theories of Strongly Interacting Electrons",

I.Ichinose and T.Matsui,

cond-mat/0008099

Physical Review Letters**86**(2001) 942.- Abstract - In a recent Letter[1], Nayak argued that slave partices are always confined in gauge theories of strongly-correlated electron systems like the t-J model. The argument mostly relies on Elitzur's theorem and the fact that the effective gauge theory under discussion is at infinite coupling. On the other hand, in the previous papers [2] we studied dynamics of the gauge theory of the t-J model showing that the slave particles are in the Coulomb phase

below certain critical temperature T_{CSS}that depends on hole doping. Thus, with a finite 3D coupling, the spin-charge separation occur, while in pure 2D, slave particles interact via logarithmic potential (in contrast to the linear-rising confining potential). We comment on the discrepancy between the results in Refs.1,2.

[1] C.Nayak, Phys. Rev. Lett.**83**178 (2000).

[2] I.Ichinose and T.Matsui, Nucl.Phys.**B394**281 (1993); Phys.Rev. B 51 (1995) 11860.

- "Gauge Symmetry and Neural Networks",

T.Matsui,

cond-mat/0112463

pp. 271-280 in "Fluctuating Paths and Fields", World Scientific (2001).- Abstract - We propose a new model of neural network. It consists of spinvariables to describe the state of neurons as in the Hopfield modeland new gauge variables to describe the state of synapses.The model possesses local gauge symmetry and resembleslattice gauge theory of high-energy physics.Time dependence of synapses describes the process of learning.The mean field theory predicts a new phase corresponding toconfinement phase, in which brain losesablility of learning and memory.

- "Spin-Gap Effect on Resistivity in the t-J Model",

M.Onoda, I.Ichinose and T.Matsui,

cond-mat/9903243

Journal of Physical Society of Japan 69 (2000) Letter 3497-3500.- Abstract - We calculate the spin-gap effect on dc resistivity in the t-J model of high-T_c cuprates by using the Ginzburg-Landau theory coupled with a gauge field as its effective field theory to get \rho(T) \propto T [1-c (T* -T)^d], where T* is the spin-gap onset temperature. By taking the compactness of massive gauge field into account, the exponent d deviates from its mean-field value 1/2 and becomes a nonuniversal T-dependent quantity, which improves the comparison with the experiments.

- "Charge-Spin Separation and the Resistivity in the Spin-Gap State",

M.Onoda, I.Ichinose and T.Matsui,

Chinese Journal of Physics 38 (2000) 306-312.- Abstract - We explain the concept of charge-spin separation (CSS) in the slave-boson t-J model for high-$T_{\rm c}$ cuprates, and, as an application of the CSS, briefly review our recent calculation of the dc resistivity in the spin-gap state.

- "Finite-Temperature Renormalization-Group Study of a Dissipative
Gauge Theory with Fermions",

T.Takano, M.Onoda, I.Ichinose and T.Matsui,

Nuclear Physics B [FS] 542 (1999) 581-620.- Abstract - We study finite temperature (T) properties of a two-dimensional system of fermions interacting with a dissipative gauge field. This system is relevant to various strongly-correlated electron systems including systems of quantum Hall effect and high-T

_{c}superconductors. At T=0, it is known that this dissipative gauge theory of fermions has a nontrivial infrared fixed point, and fermions exhibit non-Fermi-liquid like behavior. We extend the Wilson-type renormalization-group (RG) study at T=0 given in our previous paper to the finite-T case. Renormalization constants are explicitly calculated in the one-loop order at finite T and RG equations of running coupling constants are obtained. We perform numerical calculations to solve the RG recursion equations and obtain a flow diagram. In some parameter regions, our results show that the non-Fermi-liquid fixed point at T=0 becomes unstable by finite-T effects. However, in intermediate energy scales, the behavior of coupling constants is controlled by the non-Fermi-liquid fixed point at T=0, i.e., the fixed point at T=0 becomes a saddle point at T > 0. Physical implications of this phenomenon are discussed.

- "Resistivity of the Spin Gap State in the t-J Model",

M.Onoda, I.Ichinose and T.Matsui,

cond-mat/9712182

Journal of the Physical Society of Japan 67 (1998) Letter 2606-2609.- Abstract - Being motivated by recent experimental data on YBaCuO, we calculate dc resistivity \rho in the spin-gap state of charge-spin-separated t-J model by using a massive gauge theoryof holons and spinons. The result shows \rho(T) deviates downward from the T-linear behavior below the spin-gap on-set temperature T* as \rho(T) \propto T [1-c(T*-T)^d] where the mean field value of d is 1/2.To achieve smooth deviation from the T-linear behavior, one needs d > 1. The deviation becomes reduced with increasing hole doping.

- "Quasi-Excitations and Superconductivity in the t-J Model
on a Ladder",

I.Ichinose and T.Matsui,

cond-mat/97100022

Physical Review B 57 (1998) 13790-13799.- Abstract - We study the t-J model on a ladder using the slave-fermion-CP

^{1}formalism which has been used successfully in studying lightly doped high-Tc cuprates. We obtain a low-energy effective model assuming a short-range antiferromagnetic order (SRAFO), which includes gauge-field degrees of freedom because of the use of slave-particle picture. We give a systematic study on the dynamics of composite gauge bosons to show that the confinement phase is realized in a 2-leg system whereas the deconfinement phase is realized in a chain system. This explains why quasi-excitations are so different in the chain and ladder systems. The effective model also reveals attractive forces between holes, which generate d-wave type superconductive correlations in SRAFO. The low-energy excitations on a ladder are consistently described by the universality class of a Luther-Emery liquid.

- "Fluctuation Effects of Gauge Fields in the
Slave-Boson t-J Model",

I.Ichinose, T.Matsui and K.Sakakibara,

cond-mat/9701156

Journal of the Physical Society of Japan 67 (1998) 543-550.- Abstract - We present a quantitative study of the charge-spin separation (CSS) phenomenon in a U(1) gauge theory of the t-J model of high-Tc superconductors. We calculate the critical temperature Tcss of a confinement-deconfinement phase transition as a function of hole doping \delta, below which the CSS takes place. Fluctuations of gauge fields are so large that Tcss is reduced to about 10 % of its mean-field value. We also make some comments on the phase structure from a gauge-theoretical point of view.

- "Monte Carlo Study of Asymmetric 2D XY Model",

C.Holm, W.Janke, T.Matsui and K.Sakakibara,

Physica A 246 (1997) 633-645.- Abstract - Employing the Polyakov-Susskind approximation in a field theoretical treatment, the t-J model for strongly correlated electrons in two dimensions has recently been shown to map effectively onto an asymmetric two-dimensional classical XY model. The critical temperature at which charge-spin separation occurs in the t-J model is determined by the location of the phase transitions of this effective model. Here we report results of Monte Carlo simulations which map out the complete phase diagram in the two-dimensional parameter space and also shed some light on the critical behaviour of the transitions.

- "Particle-Flux Separation of Electrons in the
Half-Filled Landau Level: - Chargeon-Fluxon Approach -",

I.Ichinose and T.Matsui,

cond-mat/9606166

Nuclear Physics B [FS] 483 (1997) 681-704.- Abstract - We have previously studied the phase structure at finite temperatures of the Chern-Simons (CS) gauge theory coupled with fermions by using lattice gauge theory. In this paper, we formulate the ``chargeon-fluxon" representation of electrons and use it to reinvestigate the phenomenon of particle-flux separation (PFS) of electrons in the half-filled Landau level. We start with a lattice system of fermions interacting with a CS gauge field, and introduce two slave operators named chargeon and fluxon that carry the CS charge and flux, respectively. The original fermion, the composite fermion of Jain, is a composite of a chargeon and a fluxon. We further rewrite the model by introducing an auxiliary link field, the phase of which behaves as a gauge field gluing chargeons and fluxons. Then we study a confinement-deconfinement transition of that gauge field by using the theory of separation phenomena as in the previous paper. The residual four-fermi interactions play an important role to determine the critical temperature TPFS, below which the PFS takes place. The new representation has some advantages; (1) It allows a field-theoretical description also for the flux degrees of freedom. (2) It has a close resemblance to the slave-boson or slave-fermion representations of the t-J model of high-Tc superconductors in which an electron is a composite of a holon and a spinon. This point opens a way to understand the two typical separation phenomena in strongly-correlated electron systems in a general and common setting.

- "Theory of Separation Phenomena in
Strongly-Correlated Electron Systems",

I.Ichinose and T.Matsui,

Czechoslovak Journal of Physics 46 (1996) 1883-1884.- Abstract - We present a coherent gauge-theoretical interpretation of various possible separation phenomena of strongly-correlated electron systems. The typical examples are (i) charge-spin separation (CSS) in the t-J model of high-Tc superconductivity, and (ii) particle-flux separation (PFS) in the quantum Hall effect at = 1/2. By introducing auxiliary gauge fields, we map the system into an effective U(1) lattice gauge theory. It exhibits a confinement-deconfinement (CD) phase transition at TCD. At T > TCD, the system is in a confinement phase and the electrons themselves are quasiparticles. At T < TCD, the system is in a deconfinement phase and each constituent degrees of freedoms of electrons (holons and spinons in CSS and composite fermions and fluxes in PFS) are liberated and become independent quasiparticles.

- "Finite Temperature Properties of a Gauge Theory
of Nonrelativistic Fermions",

M. Onoda, I.Ichinose, and T.Matsui,

cond-mat/9605131

Physical Review B 54 (1996) 13674-13686.- Abstract - We study finite temperature properties of a gauge theory of nonrelativistic fermions introduced by Halperin, Lee, and Read. This gauge theory is relevant to two interesting systems: high-Tc superconductors in the anomalous metallic phase and a two-dimensional electron system in a strong magnetic field at the Landau filling factor = 1/2 . We calculate the self-energies of both gauge bosons and fermions by the random-phase approximation, showing that the dominant terms at low energies are generated by the gauge-fermion interaction. The current-current correlation function is also calculated by the ladder approximation. We confirm that the electric conductivity satisfies the Drude formula and obtain its temperature dependence, which is of a non-Fermi-liquid.

- "Mechanism of Particle-Flux Separation and
Generation of Dynamical Gauge Field in the Chern-Simons Theory with Fermions",

I.Ichinose and T.Matsui,

Nuclear Physics B 468 [FS] (1996) 487-513.- Abstract - We study the nonperturbative aspects of the Chern-Simons (CS) gauge theory coupled with fermions by using spatial-lattice regularization. This system is relevant to (i) the composite-fermion approach to the fractional quantum Hall effect, and (ii) the fermionic description of s= 1/2 quantum XY spin model. It is expected that there are (at least) two phases in this system: One is the constrained phase in which the CS constraint is respected by quasiparticles, so certain amount of gauge fluxes are to be attached to each fermion. The other is the

*dynamical*phase in which the CS constraint is irrelevant to the quasiparticles, and a dynamical gauge field is generated as an*independent*field. We call this phenomenon of irrelevance of the CS constraint to the quasiparticles a particle-flux separation (PFS), since particles and fluxes are not constrained each other. This PFS is characterized through the dynamics of an auxiliary gauge field that glues particles and CS fluxes, and bears very close resemblance to the phenomenon of charge-spin separation in the strongly-correlated electron system for high-Tc superconductivity. We show that there is a confinement-deconfinement (CD) phase transition in the gauge dynamics in question, which is of the sametype as the Kosterlitz-Thouless (KT) transition of the classical XY model in two dimensions. The critical temperature TCD is calculable and dependent on the CS coefficient and the density of fermions. The constrained phase is identified with the confinement phase of gauge dynamics at T > TCD, while the dynamical phase with PFS is identified with the deconfinement phase at T < Tc. This result is applicable to the system of electrons in a uniform magnetic field at Landau filling factor \nu = 1/2. That is, there appears a dynamical gauge field that interacts weakly with the so-called composite fermions. This justifies several existing analyses based on perturbation theory, which conclude non-Fermi-liqiud-like behavior of the fermionic quasiparticles.

- "Confinement and Deconfinement Phenomena in High-Tc
Materials and Quantum Hall State at = 1/2",

I.Ichinose and T.Matsui,

Chinese Journal of Physics 34 (1996) 392-396.- Abstract - We review first the recent gauge-theory interpretation of the phenomenon of charge-spin separation (CSS) in the t-J model. An electron is described as a compound of holon and spinon. Above certain critical temperature TCD holons and spinons are confined within electrons, while below TCD, the gauge force operating between them becomes weak and holons and spinons are deconfined and liberated. The latter case corresponds to CSS. Next, we consider the electron system in a constant magnetic field in the half-filled Landau level = 1/2). We employ Jain's composite-fermion picture (CF) in which an electron is described as a compound of CF and fluxes of Chern-Simons gauge field. By applying the method same as for CSS, we find that there exits a critical temperature TCD. Above TCD, the gauge force is confining and CF's and fluxes move together, while below TCD, the gauge force is weak and the particle-flux separation (PFS) takes places, i.e, CF's and fluxes move independently. We point out the strong parallelism between CSS and PFS and reveal the universality of gauge-theoretical interpretation.

- "Particle-Flux Separation in Chern-Simons
Theory and the Landau-Level Gap of Composite Fermions",

I.Ichinose, T.Matsui, and M. Onoda,

Physical Review B 52 (1995) 10547-10560.- Abstract - We study a system of non-relativistic fermions in a uniform magnetic field near the half-filled Landau level ( = 1/2) from a viewpoint of gauge theory. At the exact half filling, quasi-excitations are so-called composite fermions and dynamically generated gauge bosons. A composite fermion (CF) is an electron with two flux quanta attaching to it. Because of interactions between fermions and gauge bosons, there appears anormalous behavior in the fermion propagator, i.e., vanishing of Fermi velocity. We start with this picture at the half filling and follow the CF approach of Jain to the fractional quantum Hall effect near the half filling. We then make use of the Chern-Simons bosonization to describe these CF's in a residual magnetic field. We calculate the effective Landau-level gap of CF, and find that it tends to vanish near the half filling due to the dynamical gauge field. Our calculation naturally explains the recent experiments reporting that the excitation gap of quantum Hall states behaves anormalously near the half filling, i.e., enhancement of the effective mass of quasi-particles. This phenomenon can be understood by a shielding mechanism between two kinds of fluxes and the Nambu-Goldstone mode of bosonized CF's. Throughout the calculation, we assume that there are two possible phases: in one phase, particles and fluxes are bound, while in the other phase, particles and fluxes are separated, i.e., the particle-flux separation occurs.

- "Dissipative Gauge Theory of Fermions and
Its Marginal-Fermi-Liquid-Like Behavior",

M. Onoda, I.Ichinose, and T.Matsui,

Nuclear Physics B 446 [FS] (1995) 353-372.- Abstract - A non-relativistic fermion system interacting with a gauge field is studied by Wilsonian renormalization-group analysis. This model is motivated by the work of Halperin, Lee and Read, which discussed a two-dimensional electron system in a magnetic field at the Landau filling factor =1/2. A dissipative term of the gauge field (the Landau damping factor) is generated under the renormalization-group transformations, and it plays a very important role in the low-energy behaviors of the system. Renormalization constants are calculated in the one-loop level. In some parameter region, the renormalized gauge coupling constant has a non-trivial infrared fixed point, and the low-energy renormalized fermion propagator has a branch cut rather than a pole, just like the Luttinger liquid in one dimension. At a special value of the parameter, the weight of quasiparticles decreases at low energy as 1/(ln \omega), where \omega is the energy of fermion. This behavior is nothing but that of the marginal Fermi liqiud, which is proposed to describe the anomalous metallic phase of high-Tc cuprates.

- "Gauge Theory of Non-Relativistic Fermions and Its
Low-Energy Behavior",

I.Ichinose and T.Matsui,

Nuclear Physics B 441 [FS] (1995) 483-514.- Abstract - A system of (2+1) dimensional non-relativistic fermions with gauge interaction is studied by the renormalization-group analysis. Fluctuations of long-wavelength excitations of the gauge field are controlled as k^{2-b}, where k is the magnitude of momentum of gauge boson and b is a parameter of the present system. This model is motivated by the work of Halperin, Lee and Read, which discussed a (2+1)-dimensional electron system in an external magnetic field at a filling factor of Landau level = 1/2. The \beta function of gauge coupling and the anomalous dimension of fermion are systematically calculated, in the sense of (b-1)- expansion, both in the loop and the RPA - 1/N expansions (where N is the number of species of fermions). Results are different in these two calculations. In the loop expansion, there appears a non-trivial IR fixed point of gauge coupling for b < 1, but the anormalous dimension of fermion is vanishing. On the other hand, in the RPA calculation, renormalization of the gauge-fermion vertex does not occur, while the fermion wave function is renormalized because of a dissipative term in the dressed gauge propagator. These results are systematically understood by the Ward-Takahashi identity reflecting gauge invariance. Our calculations are compared with the recent work of Nayak and Wilczek.

- "Charge-Spin Separation in the t-J Model:
An Effective-Field-Theory Approach",

T.Matsui,

Synthetic Metals 71 (1995) 1643-1644.- Abstract - A low-energy effective field theory of the t-J model for the normal state and the antiferromagnetic state is derived in the slave-fermion representation assuming a short-range antiferromagnetic order. It takes a form of the nonlinear CP

^{1}sigma model of spins coupled with the nonrelativistic fermion for doped holes in a U(1) gauge-invariant manner. The renormalization-group equations on the one-loop level are calculated a la Polyakov's prescription. It is discussed how the possible charge-spin separation phenomenon of cuprate high-Tc superconductors may be described in terms of the renormalization group of the effective field theory.

- "Mechanism of the Charge-Spin Separation in
the t-J Model: Dynamics of U(1) Gauge Theory with Multiple
Gauge Fields",

I.Ichinose and T.Matsui,

Physical Review B 51 (1995) 11860-11881.- Abstract - Mechanism of the charge-spin separation (CSS) in the t-J model, both in the slave-boson and the slave-fermion representations, is studied in detail from the view point of gauge theory. Dynamics of composite gauge bosons, i.e., of phase degrees of freedom of mean fields defined on links, is carefully analyzed. The Polyakov-Susskind theory of the confinement-deconfinement (CD) phase transition plays an essential role in this analysis. As we showed generally in our previous paper, the CSS phase corresponds to the deconfinement phase of gauge theory of mean field. The quasi-particles here are holons, spinons and gauge bosons. Across the CD transition, another phase, the electron phase, is realised, which corresponds to the confinement phase of gauge theory. The quasi-particles in this phase are conventional electrons, which may be viewed as bound states of holons and spinons. In this paper, we demonstrate that the two-dimensional t-J model exhibits the phenomenon of CSS

*below*certain critical temperature TCD, the CD transition temperature, and calculate TCD as a function of hole concentration. Most important contribution to the realization of CSS comes from non-relativistic gapless excitations via screening of confining potential among holons and spinons. Reflecting upon two kinds of mean fields, i.e., in the normal and super channels, the resulting CSS-deconfinement phase of the t-J model is further classified into Coulomb phase and Higgs phase. By applying the Polyakov-Susskind theory, they are described by the spin-ordered phase of the isotropic and of the anisotropic XY spin model, respectively.