論文

Transport properties in the presence of magnetic fields are numerically studied for the spin-1/2 Heisenberg XXZ chain. The breakdown of the spin-reversal symmetry due to the magnetic field induces the magnetothermal effect. In analogy with the thermoelectric effect in electron systems, the thermomagnetic power (magnetic Seebeck coefficient) is provided, and is numerically evaluated by the exact diagonalization for wide ranges of temperatures and various magnetic fields. For the antiferromagnetic regime, we find the magnetic Seebeck coefficient changes sign at certain temperatures, which is interpreted as an effect of strong correlations. We also compute the thermomagnetic figure of merit determining the efficiency of the thermomagnetic devices for cooling or power generation. ©2005 The Physical Society of Japan.

A characterization of topological order in terms of bi-partite entanglement was proposed recently. It was argued that in a topological phase there is a universal additive constant in the entanglement entropy, called the topological entanglement entropy, which reflects the underlying gauge theory for the topological order. In the present paper, we evaluate numerically the topological entanglement entropy in the ground states of a quantum dimer model on the triangular lattice, which is known to have a dimer liquid phase with Z2 topological order. We examine the two original constructions to measure the topological entropy by combining entropies on plural areas, and we observe that in the large-area limit they both approach the value expected for Z2 topological order. We also consider the entanglement entropy on a topologically nontrivial "zigzag" area and propose to use it as another way to measure the topological entropy. © 2007 The American Physical Society.

We present a quantum theory for one-dimensional spin-1/2 multiferroics, where the vector spin chirality couples with the electric polarization. Based on exact diagonalization and bosonization, it is shown that quantum fluctuations appreciably reduce the chiral ordering amplitude and the associated ferroelectric polarization. This yields nearly collinear spin correlations in short-range scales, in qualitative agreement with recent neutron scattering experiments. There appear gapless chirality excitations described by phasons and new solitons, which can be experimentally verified from the low-energy dielectric response. ©2008 The Physical Society of Japan.

We study the generic scaling properties of the mutual information between two disjoint intervals, in a class of one-dimensional quantum critical systems described by the c=1 bosonic field theory. A numerical analysis of a spin-chain model reveals that the mutual information is scale invariant and depends directly on the boson radius. We interpret the results in terms of correlation functions of branch-point twist fields. The present study provides a new way to determine the boson radius, and furthermore demonstrates the power of the mutual information to extract more refined information of conformal field theory than the central charge. © 2009 The American Physical Society.

We study the Shannon entropy of the probability distribution resulting from the ground-state wave function of a one-dimensional quantum model. This entropy is related to the entanglement entropy of a Rokhsar-Kivelson-type wave function built from the corresponding two-dimensional classical model. In both critical and massive cases, we observe that it is composed of an extensive part proportional to the length of the system and a subleading universal constant S0. In c=1 critical systems (Tomonaga-Luttinger liquids), we find that S0 is a simple function of the boson compactification radius. This finding is based on a field-theoretical analysis of the Dyson-Gaudin gas related to dimer and Calogero-Sutherland models. We also performed numerical demonstrations in the dimer models and the spin-1/2 XXZ chain. In a massive (crystal) phase, S0 is related to the ground-state degeneracy. We also examine this entropy in the Ising chain in a transverse field as an example showing a c=1/2 critical point. © 2009 The American Physical Society.

We study two-component (or pseudo-spin-12) Bose or Fermi gases in one dimension, in which particles are convertible between the components. Through bosonization and numerical analyses of a simple lattice model, we demonstrate that, in such gases, a strong intercomponent repulsion induces spontaneous population imbalance between the components, namely, the ferromagnetism of the pseudo spins. The imbalanced phase contains gapless charge excitations characterized as a Tomonaga-Luttinger liquid and gapped spin excitations. We uncover a crucial effect of the intercomponent particle hopping on the transition to the imbalanced phase. In the absence of this hopping, the transition is of first order. At the transition point, the energy spectrum reveals certain degeneracy indicative of an emergent SU(2) symmetry. With an infinitesimal intercomponent hopping, the transition becomes of Ising type. We determine the phase diagram of the model accurately and test the reliability of the weak-coupling bosonization formalism. © 2010 The American Physical Society.

We investigate strongly correlated phases of two-component (or pseudospin-1/2) Bose gases under rapid rotation through exact diagonalization on a torus geometry. In the case of pseudospin-independent contact interactions, we find the formation of gapped spin-singlet states at the filling factors ν=k/3+k/3 (k/3 filling for each component) with integer k. We present numerical evidences that the gapped state with k=2 is well described as a non-Abelian spin-singlet (NASS) state, in which excitations feature non-Abelian statistics. Furthermore, we find the phase transition from the product of composite fermion states to the NASS state by changing the ratio of the intercomponent-to-intracomponent interactions. © 2012 American Physical Society.

We study two-component (or pseudospin-1/2) Bose gases in a strong synthetic magnetic field. Using exact diagonalization, we show that a bosonic analog of an integer quantum Hall state with no intrinsic topological order appears at the total filling factor ν=1+1 when the strengths of intracomponent and intercomponent interactions are comparable with each other. This provides a prime example of a symmetry-protected topological phase in a controlled setting of quantum gases. The real-space entanglement spectrum of this state is found to be comprised of counterpropagating chiral modes consistent with the edge theory derived from an effective Chern-Simons theory. © 2013 American Physical Society.

We study the entanglement spectrum (ES) and entropy between two coupled Tomonaga-Luttinger liquids (TLLs) on parallel periodic chains. This problem gives access to the entanglement properties of various interesting systems, such as spin ladders as well as two-dimensional topological phases. By expanding interchain interactions to quadratic order in bosonic fields, we are able to calculate the ES for both gapped and gapless systems using only methods for free theories. In certain gapless phases of coupled nonchiral TLLs, we interestingly find an ES with a dispersion relation proportional to the square root of the subsystem momentum, which we relate to a long-range interaction in the entanglement Hamiltonian. We numerically demonstrate the emergence of this unusual dispersion in a model of hard-core bosons on a ladder. In gapped phases of coupled nonchiral TLLs, which are relevant to spin ladders and topological insulators, we show that the ES consists of linearly dispersing modes, which resembles the spectrum of a single-chain TLL but is characterized by a modified TLL parameter. Based on a calculation for coupled chiral TLLs, we are also able to provide a very simple proof for the correspondence between the ES and the edge-state spectrum in quantum Hall systems consistent with previous numerical and analytical studies. © 2013 American Physical Society.

© 2014 American Physical Society. We study the ground-state phase diagram of two-dimensional two-component (or pseudospin-12) Bose gases in mutually antiparallel synthetic magnetic fields in the space of the total filling factor and the ratio of the intercomponent coupling g↑↓ to the intracomponent coupling g>0. This time-reversal-invariant setting represents a bosonic analog of spin Hall systems. Using exact diagonalization, we find that (fractional) quantum spin Hall states composed of a pair of nearly independent quantum Hall states are remarkably robust and persist for g↑↓ up to as large as g. For g↑↓=-g, we find the exact many-body ground state in which particles in different spin states form pairs. This gives the exact critical line beyond which the system collapses in the thermodynamic limit.

© 2015 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. We show that Bose-Einstein condensates in optical lattices with broken time-reversal symmetry can support chiral edge modes originating from nontrivial bulk excitation band topology. To be specific, we analyze a Bose-Hubbard extension of the Haldane model, which can be realized with recently developed techniques of periodically modulating honeycomb optical lattices. The topological properties of Bloch bands known for the noninteracting case are shown to be smoothly carried over to Bogoliubov excitation bands for the interacting case. We show that the parameter ranges that display topological bands enlarge with increasing the Hubbard interaction or the particle density. In the presence of sharp boundaries, chiral edge modes appear in the gap between topological excitation bands. We demonstrate that by coherently transferring a portion of a condensate into an edge mode, a density wave is formed along the edge owing to an interference with the background condensate. This offers a unique method of detecting an edge mode through a macroscopic quantum phenomenon.

© 2016 American Physical Society. Motivated by recent experiments on volborthite single crystals showing a wide 13-magnetization plateau, we perform microscopic modeling by means of density functional theory (DFT) with the single-crystal structural data as a starting point. Using DFT+U, we find four leading magnetic exchanges: antiferromagnetic J and J2, as well as ferromagnetic J′ and J1. Simulations of the derived spin Hamiltonian show good agreement with the experimental low-field magnetic susceptibility and high-field magnetization data. The 13-plateau phase pertains to polarized magnetic trimers formed by strong J bonds. An effective J→ model shows a tendency towards condensation of magnon bound states preceding the plateau phase.

© 2016 American Physical Society. We study strongly correlated ground states of dipolar fermions in a honeycomb optical lattice with spatial variations in hopping amplitudes. Similar to strained graphene, such nonuniform hopping amplitudes produce valley-dependent pseudomagnetic fields for fermions near the two Dirac points, resulting in the formation of Landau levels. The dipole moments aligned perpendicular to the honeycomb plane yield a long-range repulsive interaction. By exact diagonalization in the zeroth-Landau-level basis, we show that this repulsive interaction stabilizes a variety of valley-polarized fractional quantum Hall states such as Laughlin and composite-fermion states. The present system thus offers an intriguing platform for emulating fractional quantum Hall physics in a static optical lattice. We calculate the energy gaps above these incompressible states and discuss the temperature scales required for their experimental realization.

©2016 American Physical Society. Recent realizations of quantum gas microscopy offer the possibility of continuous monitoring of the dynamics of a quantum many-body system at the single-particle level. By analyzing effective non-Hermitian Hamiltonians for interacting bosons in an optical lattice and continuum, we demonstrate that the backaction of quantum measurement shifts the quantum critical point and gives rise to a unique critical phase beyond the terrain of the standard universality class. We perform mean-field and strong-coupling-expansion analyses and show that non-Hermitian contributions shift the superfluid-Mott-insulator transition point. Using a low-energy effective field theory, we discuss critical behavior of the one-dimensional interacting Bose gas subject to the measurement backaction. We derive an exact ground state of the effective non-Hermitian Hamiltonian and find a unique critical behavior beyond the Tomonaga-Luttinger liquid universality class. We propose experimental implementations of postselections using a quantum gas microscope to simulate the non-Hermitian dynamics and argue that our results can be investigated with current experimental techniques in ultracold atoms.

© 2017 American Physical Society. We study interacting bosonic or fermionic atoms in a high synthetic magnetic field in two dimensions spanned by continuous real space and a synthetic dimension. Here the synthetic dimension is provided by hyperfine spin states, and the synthetic field is created by laser-induced transitions between them. While the interaction is short-range in real space, it is long-range in the synthetic dimension in sharp contrast with fractional quantum Hall systems. Introducing an analog of the lowest-Landau-level approximation valid for large transition amplitudes, we derive an effective one-dimensional lattice model, in which density-density interactions turn out to play a dominant role. We show that in the limit of a large number of internal states, the system exhibits a cascade of crystal ground states, which is known as the devil's staircase, in a way analogous to the thin-torus limit of quantum Hall systems.

© 2017 American Physical Society. Based on a quasi-one-dimensional limit of quantum Hall states on a thin torus, we construct a model of interaction-induced topological pumping which mimics the Hall response of the bosonic integer quantum Hall (BIQH) state. The quasi-one-dimensional counterpart of the BIQH state is identified as the Haldane phase composed of two-component bosons which form effective spin-1 degrees of freedom. An adiabatic change between the Haldane phase and trivial Mott insulators constitutes off-diagonal topological pumping in which the translation of the lattice potential for one component induces a current in the other. The mechanism of this pumping is interpreted in terms of changes in polarizations between symmetry-protected quantized values.

© The Author(s) 2017. Synthetic non-conservative systems with parity-time (PT) symmetric gain-loss structures can exhibit unusual spontaneous symmetry breaking that accompanies spectral singularity. Recent studies on PT symmetry in optics and weakly interacting open quantum systems have revealed intriguing physical properties, yet many-body correlations still play no role. Here by extending the idea of PT symmetry to strongly correlated many-body systems, we report that a combination of spectral singularity and quantum criticality yields an exotic universality class which has no counterpart in known critical phenomena. Moreover, we find unconventional low-dimensional quantum criticality, where superfluid correlation is anomalously enhanced owing to non-monotonic renormalization group flows in a PT-symmetry-broken quantum critical phase, in stark contrast to the Berezinskii-Kosterlitz-Thouless paradigm. Our findings can be experimentally tested in ultracold atoms and predict critical phenomena beyond the Hermitian paradigm of quantum many-body physics.

© 2017 American Physical Society. We propose that the properties of the capacity of entanglement (COE) in gapless systems can efficiently be investigated through the use of the distribution of eigenvalues of the reduced density matrix (RDM). The COE is defined as the fictitious heat capacity calculated from the entanglement spectrum. Its dependence on the fictitious temperature can reflect the low-temperature behavior of the physical heat capacity and thus provide a useful probe of gapless bulk or edge excitations of the system. Assuming a power-law scaling of the COE with an exponent α at low fictitious temperatures, we derive an analytical formula for the distribution function of the RDM eigenvalues. We numerically test the effectiveness of the formula in a relativistic free scalar boson in two spatial dimensions and find that the distribution function can detect the expected α=3 scaling of the COE much more efficiently than the raw data of the COE. We also calculate the distribution function in the ground state of the half-filled Landau level with short-range interactions and find better agreement with the α=2/3 formula than with the α=1 one, which indicates a non-Fermi-liquid nature of the system.

© 2017 American Physical Society. We study the ground-state phase diagram of two-dimensional two-component (or pseudospin-12) Bose gases in a high synthetic magnetic field in the space of the total filling factor and the ratio of the intercomponent coupling g↑↓ to the intracomponent one g>0. Using exact diagonalization, we find that when the intercomponent coupling is attractive (g↑↓<0), the product states of a pair of nearly uncorrelated quantum Hall states are remarkably robust and persist even when |g↑↓| is close to g. This contrasts with the case of an intercomponent repulsion, where a variety of spin-singlet quantum Hall states with high intercomponent entanglement emerge for g↑↓≈g. We interpret this marked dependence on the sign of g↑↓ in light of pseudopotentials on a sphere, and also explain recent numerical results in two-component Bose gases in mutually antiparallel magnetic fields where a qualitatively opposite dependence on the sign of g↑↓ is found. Our results thus unveil an intriguing connection between multicomponent quantum Hall systems and quantum spin Hall systems in minimal setups.

© 2019 The Author(s). Published by IOP Publishing Ltd on behalf of Deutsche Physikalische Gesellschaft. We study collective modes of vortex lattices in two-component Bose-Einstein condensates subject to synthetic magnetic fields in mutually parallel or antiparallel directions. By means of the Bogoliubov theory with the lowest-Landau-level approximation, we numerically calculate the excitation spectra for a rich variety of vortex lattices that appear commonly for parallel and antiparallel synthetic fields. We find that in all of these cases there appear two distinct modes with linear and quadratic dispersion relations at low energies, which exhibit anisotropy reflecting the symmetry of each lattice structure. Remarkably, the low-energy spectra for the two types of fields are found to be related to each other by simple rescaling when vortices in different components overlap owing to an intercomponent attraction. These results are consistent with an effective field theory analysis. However, the rescaling relations break down for interlaced vortex lattices appearing with an intercomponent repulsion, indicating a nontrivial effect of an intercomponent vortex displacement beyond the effective field theory. We also find that high-energy parts of the excitation bands exhibit line or point nodes as a consequence of a fractional translation symmetry present in some of the lattice structures.