Gauged Gross--Neveu model with overlap fermions

We investigate chiral properties of the overlap lattice fermion by using solvable model in two dimensions, the gauged Gross-Neveu model. In this model, the chiral symmetry is spontaneously broken in the presence of small but finite fermion mass. We calculate the quasi-Nambu-Goldstone(NG) boson mass as a function of the bare fermion mass and two parameters in the overlap formula. We find that the quasi-NG boson mass has desired properties as a result of the extended chiral symmetry found by L\"uscher. We also show the PCAC relation is satisfied in desired form. Comparison between the overlap and Wilson lattice fermions is also made.Comment: Latex 9 pages, sty file included, talk by K.Nagao at Chiral'99, Taipei, Taiwan, Sep.13-18, 1999. (To be pubished in the Proceedings) Typo correcte

Lattice Gauge Theory for Condensed Matter Physics: Ferromagnetic Superconductivity as its Example

Recent theoretical studies of various strongly-correlated systems in condensed matter physics reveal that the lattice gauge theory(LGT) developed in high-energy physics is quite a useful tool to understand physics of these systems. Knowledges of LGT are to become a necessary item even for condensed matter physicists. In the first part of this paper, we present a concise review of LGT for the reader who wants to understand its basics for the first time. For illustration, we choose the abelian Higgs model, a typical and quite useful LGT, which is the lattice verison of the Ginzburg-Landau model interacting with a U(1) gauge field (vector potential). In the second part, we present an account of the recent progress in the study of ferromagnetic superconductivity (SC) as an example of application of LGT to topics in condensed matter physics, . As the ferromagnetism (FM) and SC are competing orders with each other, large fluctuations are expected to take place and therefore nonperturbative methods are required for theoretical investigation. After we introduce a LGT describing the FMSC, we study its phase diagram and topological excitations (vortices of Cooper pairs) by Monte-Carlo simulations.Comment: 31 pages, 13 figures, Invited review article of Mod.Phys.Lett.

Gross-Neveu model with overlap fermions

We investigate the chiral properties of overlap lattice fermion by using two dimensional Gross-Neveu model coupled with a gauge field. Chiral properties of this model are similar to those of QCD$_4$, that is, the chiral symmetry is spontaneously broken in the presence of small but finite fermion mass and also there appears the chiral anomaly because of the coupling with the gauge field. In order to respect L\"uscher's extended chiral symmetry we insert overlap Dirac operator even in the interaction terms so that the whole action including them are invariant under the extended chiral transformation at {\em finite lattice spacing}, though the interaction terms become nonlocal. We calculate mass of the quasi-Nambu-Goldstone boson as a function of the bare fermion mass and two parameters in the overlap formalism, and find that the quasi-Nambu-Goldstone boson has desired properties as a result of the extended chiral symmetry. We furthermore examine the PCAC relation and find that it is satisfied at {\em finite lattice spacing}. Relationship between the anomaly term in the PCAC relation and the U(1) problem is also discussed.Comment: Latex 12 pages, typo corrected, title changed, the flavor-singlet eta mass calculated, discussion of the relationship between U(1) problem and chiral anomaly added, the published version in Mod.Phys.Lett.

Nonlocally-Correlated Disorder and Delocalization in One Dimension: Density of States

We study delocalization transition in a one-dimensional electron system with quenched disorder by using supersymmetric (SUSY) methods. Especially we focus on effects of nonlocal correlation of disorder, for most of studies given so far considered $\delta$-function type white noise disorder. We obtain wave function of the "lowest-energy" state which dominates partition function in the limit of large system size. Density of states is calculated in the scaling region. The result shows that delocalization transition is stable against nonlocal short-ranged correlation of disorder. Especially states near the band center are enhanced by the correlation of disorder which partially suppresses random fluctuation of disorder. Physical picture of the localization and the delocalization transition is discussed.Comment: 25 pages, LaTeX, 2 eps-figures include

Pions in Lattice QCD with the Overlap Fermions at Strong Gauge Coupling

In the previous paper we developed a strong-coupling expansion for the lattice QCD with the overlap fermions and showed that L\"usher's "extended" chiral symmetry is spontaneously broken in some parameter region of the overlap fermions. In this paper, we obtain a low-energy effective action and show that there exist quasi-Nambu-Goldsone bosons which are identified as the pions. The pion field is a {\em nonlocal} composite field of quark and anti-quark even at the strong-coupling limit because of the nonlocality of the overlap fermion formalism and L\"usher's chiral symmetry. The pions become massless in the limit of the vanishing bare-quark mass as it is desired.Comment: Latex 11 page

Particle-Flux Separation and Quasiexcitations in Quantum Hall Systems

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.Comment: 4pages, 1figur

Various Topological Mott insulators in strongly-interacting boson system in one-dimensional superlattice

In this paper, we study a one-dimensional boson system in a superlattice potential.This system is experimentally feasible by using ultracold atomic gases,and attracts much attention these days. It is expected that the system has a topological phase called topological Mott insulator (TMI). We show that in strongly-interacting cases, the competition between the superlattice potential and the on-site interaction leads to various TMIs with non-vanishing integer Chern number. Compared to hard-core case, the soft-core boson system exhibits rich phase diagrams including various non-trivial TMIs. By using the exact diagonalization,we obtain detailed bulk-global phase diagrams including the TMIs with high Chern numbers and also various non-topological phases. We also show that in adiabatic experimental setups, the strongly-interacting bosonic TMIs exhibit the topological particle transfer, i.e., topological charge pumping phenomenon, similarly to weakly-interacting systems. The various TMIs are characterized by topological charge pumping as it is closely related to the Chern number, and therefor the Chern number is to be observed in feasible experiments.Comment: 19 pages, 11 figures. Accepted for publication in New Journal of Physic

Flat-band many-body localization and ergodicity breaking in the Creutz ladder

We study disorder-free many-body localization in the flat-band Creutz ladder, which was recently realized in cold-atoms in an optical lattice. In a non-interacting case, the flat-band structure of the system leads to a Wannier wavefunction localized on four adjacent lattice sites. In the flat-band regime both with and without interactions, the level spacing analysis exhibits Poisson-like distribution indicating the existence of disorder-free localization. Calculations of the inverse participation ratio support this observation. Interestingly, this type of localization is robust to weak disorders, whereas for strong disorders, the system exhibits a crossover into the conventional disorder-induced many-body localizated phase. Physical picture of this crossover is investigated in detail. We also observe non-ergodic dynamics in the flat-band regime without disorder. The memory of an initial density wave pattern is preserved for long times.Comment: 24 pages, 14 figures, accepted version, to appear in New Journal of Physic

Vortex dynamics in lattice Bose gases in a synthesized magnetic field with a random noise and a dissipation: Study by the stochastic Gross-Pitaevskii equation

In this paper, we investigate vortex dynamics in a two-dimensional Bose-Hubbard model coupled with a weak artificial magnetic field, a random white noise and a dissipation. Origin of the noise and dissipation is considered as thermal fluctuations of atoms that do not participate the Bose-Einstein condensation (BEC). Solving a stochastic Gross-Pitaevskii equation to this system, we show that the interplay of the magnetic field and the white noise generates vortices in the bulk of the BEC and stable steady states of vortices form after a transition period. We calculate the incompressible part of the kinetic-energy spectrum of the BEC. In the transition period, a Kolmogorov $k^{-5/3}$ spectrum appears in the infrared regime with the wave number $k$, $k<\zeta^{-1}$, where $\zeta$ is the healing length, whereas in the ultraviolet region, $k>\zeta^{-1}$, the spectrum behaves as $k^{-3}$. On the other hand in the steady states, another scaling low appears. We find a relationship between the above mentioned kinetic-energy spectra and the velocity of vortices. By an inverse cascade, the large velocity of a few created vortices develops the Kolmogorov $k^{-5/3}$ spectrum.Comment: 11 pages, 8 figure

Glassy Dynamics from Quark Confinement: Atomic Quantum Simulation of Gauge-Higgs Model on Lattice

In the previous works, we proposed atomic quantum simulations of the U(1) gauge-Higgs model by ultra-cold Bose gases. By studying extended Bose-Hubbard models (EBHMs) including long-range repulsions, we clarified the locations of the confinement, Coulomb and Higgs phases. In this paper, we study the EBHM with nearest-neighbor repulsions in one and two dimensions at large fillings by the Gutzwiller variational method. We obtain phase diagrams and investigate dynamical behavior of electric flux from the gauge-theoretical point of view. We also study if the system exhibits glassy quantum dynamics in the absence and presence of quenched disorder. We explain that the obtained results have a natural interpretation in the gauge theory framework. Our results suggest important perspective on many-body localization in strongly-correlated systems. They are also closely related to anomalously slow dynamics observed by recent experiments performed on Rydberg atom chain, and our study indicates existence of similar phenomenon in two-dimensional space