Authorship：Last author,　Corresponding author   Publishing type：Research paper (scientific journal)   Publisher：Physical Society of Japan  

Hermitian topological materials are characterized by the nontrivial relation
between topological numbers and edge modes, i.e. the bulk-boundary
correspondence. In non-Hermitian systems, the conventional correspondence
breaks down. Instead, in the non-Hermitian Su-Schrieffer-Heeger model, the
non-Bloch bulk-boundary correspondence, which is the relation between the
non-Bloch winding number and the non-Hermitian skin effect, is proposed by S.
Yao and Z. Wang. We introduce the non-Bloch polarization as a topological
quantity to detect the non-Hermitian skin effect. Moreover, we also discuss the
non-Bloch bulk-boundary correspondence in two-dimensional systems using the
non-Bloch polarization with spiral boundary conditions.

DOI： 10.7566/jpsj.91.114705

arXiv

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Authorship：Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Physical Society of Japan  

DOI： 10.7566/jpsj.91.043701

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Authorship：Lead author,　Corresponding author   Publishing type：Research paper (scientific journal)   Publisher：American Physical Society (APS)  

DOI： 10.1103/physrevb.104.l121114

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Other Link： http://harvest.aps.org/v2/journals/articles/10.1103/PhysRevB.104.L121114/fulltext

Language：English  

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We discuss the polarization amplitude of quantum spin systems in one dimension. In particular, we closely investigate it in gapless phases of those systems based on the two-dimensional conformal field theory. The polarization amplitude is defined as the ground-state average of a twist operator which induces a large gauge transformation attaching the unit amount of the U(1) flux to the system. We show that the polarization amplitude under the periodic boundary condition is sensitive to perturbations around the fixed point of the renormalization-group flow rather than the fixed point itself even when the perturbation is irrelevant. This dependence is encoded into the scaling law with respect to the system size. In this paper, we show how and why the scaling law of the polarization amplitude encodes the information of the renormalization-group flow. In addition, we show that the polarization amplitude under the antiperiodic boundary condition is determined fully by the fixed point in contrast to that under the periodic one and that it visualizes clearly the nontriviality of spin systems in the sense of the Lieb-Schultz-Mattis theorem.

DOI： 10.1103/PhysRevB.99.144426

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We discuss expectation values of the twist operator U appearing in the Lieb-Schultz-Mattis theorem (or the polarization operator for periodic systems) in excited states of the one-dimensional correlated systems Z(L)((q,+/-)) <Psi(+/-)(q/2)vertical bar U-q vertical bar Psi(+/-)(q/2)>, where vertical bar Psi(+/-)(p)> denotes the excited states given by linear combinations of momentum 2pk(F) with parity +/- 1. We found that Z(L)((q,)(+/-)) gives universal values +/- 1/2 on the Tomonaga-Luttinger (TL) fixed point, and its signs identify the topology of the dominant phases. Therefore, this expectation value changes between +/- 1/2 discontinuously at a phase transition point with the U(1) or SU(2) symmetric Gaussian universality class. This means that Z(L)((q,)(+/-)) extracts the topological information of TL liquids. We explain these results based on the freefermion picture and the bosonization theory, and also demonstrate them in several physical systems.

DOI： 10.1103/PhysRevB.99.075128

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Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1140/epjb/e2018-90352-9

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We synthesized single crystals of composition Ba2CuSi2O6Cl2 and investigated their quantum magnetic properties. The crystal structure is closely related to that of the quasi-two-dimensional (2D) dimerized magnet BaCuSi2O6 also known as Han purple. Ba2CuSi2O6Cl2 has a singlet ground state with an excitation gap of Delta/k(B) = 20.8 K. The magnetization curves for two different field directions almost perfectly coincide when normalized by the g factor except for a small jump anomaly for a magnetic field perpendicular to the c axis. The magnetization curve with a nonlinear slope above the critical field is in excellent agreement with exact-diagonalization calculations based on a 2D coupled spin-dimer model. Individual exchange constants are also evaluated using density functional theory (DFT). The DFT results demonstrate a 2D exchange network and weak frustration between interdimer exchange interactions, supported by weak spin-lattice coupling implied from our magnetostriction data. The magnetic-field-induced spin ordering in Ba2CuSi2O6Cl2 is described as the quasi-2D Bose-Einstein condensation of triplets.

DOI： 10.1103/PhysRevB.94.094421

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We discuss dynamic spin susceptibility (DSS) in two-dimensional (2D) Dirac electrons with spin-orbit interactions to characterize topological insulators. The imaginary part of the DSS appears as an absorption rate in response to a transverse ac magnetic field, just as in an electron spin resonance experiment for localized spin systems. We found that when the system is in a static magnetic field, the topological state can be identified by an anomalous resonant peak of the imaginary part of the DSS as a function of the frequency of the transverse magnetic field omega. In the absence of a static magnetic field, the imaginary part of the DSS becomes a continuous function of omega with a threshold frequency omega(c). In this case, the topological and the trivial phases can also be distinguished by the values of omega(c) and by the line shapes. Thus the DSS is an experimentally observable physical quantity to characterize a topological insulator directly from bulk properties, without observing a topological transition.

DOI： 10.1103/PhysRevB.94.081411

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：American Physical Society  

The S=1 antiferromagnetic Heisenberg model on a kagome lattice is studied using the density-matrix renormalization-group method. To identify the ground state, we take four kinds of clusters into account
periodic, cylindrical, and two open ones. The hexagonal-singlet solid (HSS) and triangular valence-bond solid (TVBS) states are artificially generated by modulating edge shapes of the open clusters. We find that the energy per site of the HSS state is e0=E0/(NJ)=-1.41095, which is readily lower than that of the TVBS state (e0=-1.3912±0.0025). This agrees well with those of the cylindrical (e0=-1.4122) and periodic (e0=-1.4111) clusters where no assumption as to the ordering is posed. We further calculate the dimer-dimer correlation functions as well as the entanglement entropy of cylindrical clusters and conclude that a non-symmetry-breaking state is the ground state of the S=1 kagome Heisenberg model. Finally, we estimate the singlet-triplet energy gap: The HSS state has Δ/J=0.178±0.005, whereas the higher TVBS state has a larger one Δ/J=0.280.

DOI： 10.1103/PhysRevB.92.140412

Scopus

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

The S = 1 antiferromagnetic Heisenberg model on a kagome lattice is studied using the density-matrix renormalization-group method. To identify the ground state, we take four kinds of clusters into account; periodic, cylindrical, and two open ones. The hexagonal-singlet solid (HSS) and triangular valence-bond solid (TVBS) states are artificially generated by modulating edge shapes of the open clusters. We find that the energy per site of the HSS state is e(0) = E-0/(NJ) = -1.410 95, which is readily lower than that of the TVBS state (e(0) = -1.3912 +/- 0.0025). This agrees well with those of the cylindrical (e(0) = -1.4122) and periodic (e(0) = -1.4111) clusters where no assumption as to the ordering is posed. We further calculate the dimer-dimer correlation functions as well as the entanglement entropy of cylindrical clusters and conclude that a non-symmetry-breaking state is the ground state of the S = 1 kagome Heisenberg model. Finally, we estimate the singlet-triplet energy gap: The HSS state has Delta/J = 0.178 +/- 0.005, whereas the higher TVBS state has a larger one Delta/J = 0.280.

DOI： 10.1103/PhysRevB.92.140412

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Language：English   Publishing type：Research paper (international conference proceedings)  

DOI： 10.7566/JPSCP.4.013002

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Language：Japanese   Publisher：The Physical Society of Japan (JPS)  

DOI： 10.11316/jpsgaiyo.70.1.0_1355

CiNii Books

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Language：Japanese   Publishing type：Research paper (other academic)   Publisher：The Physical Society of Japan (JPS)  

We introduce one-dimensional lattice models with exact matrix-product ground states describing the fractional quantum Hall states in Laughlin series (given by filling factors ν=1/q) on torus geometry. The obtained exact ground states well describe properties of the Laughlin wave function. Using the matrix product method, density functions and correlation functions are calculated analytically. Especially, obtained entanglement spectra reflect properties of chiral Tomonaga Luttinger liquid of the gapless edge states.

CiNii Books

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We discuss spin-S antiferromagnetic Heisenberg chains with three-spin interactions, next-nearest-neighbor interactions, and bond alternation. First, we prove rigorously that there exist parameter regions of the exact dimerized ground state in this system. This is a generalization of the Majumdar-Ghosh model to arbitrary S. Next, we discuss the ground-state phase diagram of the models by introducing several effective field theories and the universality classes of the transitions are described by the level-2S SU(2) Wess-Zumino-Witten model and the Gaussian model. Finally, we determine the phase diagrams of S = 1 and S = 3/2 systems by using exact diagonalization and level spectroscopy.

DOI： 10.1103/PhysRevB.88.224419

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We introduce one-dimensional lattice models with exact matrix-product ground states describing the fractional quantum Hall (FQH) states in Laughlin series (given by filling factors nu = 1/q) on torus geometry. Surprisingly, the exactly solvable Hamiltonian has the same mathematical structure as that of the pseudopotential for the Laughlin wave function, and naturally derives the general properties of the Laughlin wave function such as the Z(2) properties of the FQH states and the fermion-boson relation. The obtained exact ground states have high overlaps with the Laughlin states and well describe their properties. Using the matrix product method, density functions and correlation functions are calculated analytically. Especially, obtained entanglement spectra reflect gapless edge states as was discussed by Li and Haldane.

DOI： 10.1103/PhysRevB.87.245119

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We discuss the relationship between fractional quantum Hall (FQH) states at filling factor nu = p/(2mp + 1) and quantum spin chains. This series corresponds to the Jain series nu = p/(2mp + 1) with m = 1 where the composite fermion picture is realized. We show that the FQH states with toroidal boundary conditions beyond the thin-torus limit can be mapped to effective quantum spin S = 1 chains with p spins in each unit cell. We calculate energy gaps and the correlation functions for both the FQH systems and the corresponding effective spin chains, using exact diagonalization and the infinite time-evolving block decimation (iTEBD) algorithm. We confirm that the mass gaps of these effective spin chains are decreased as p is increased which is similar to S = p integer Heisenberg chains. These results shed new light on a link between the hierarchy of FQH states and the Haldane conjecture for quantum spin chains.

DOI： 10.1103/PhysRevB.86.155104

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We introduce an exactly solvable fermion chain that describes a v = 1/3 fractional quantum Hall (FQH) state beyond the thin-torus limit. The ground state of our model is shown to be unique for each center-of-mass sector, and it has a matrix product representation that enables us to exactly calculate order parameters, correlation functions, and entanglement spectra. The ground state of our model shows striking similarities with the BCS wave functions and quantum spin-1 chains. Using the variational method with matrix product ansatz, we analytically calculate excitation gaps and vanishing of the compressibility expected in the FQH state. We also show that the above results can be related to a v = 1/2 bosonic FQH state.

DOI： 10.1103/PhysRevLett.109.016401

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We study interlayer transport of multilayer graphenes in a magnetic field with various stacking structures (AB, ABC, and AA types) by calculating the Hall and longitudinal conductivities as functions of the Fermi energy. Their behavior depends strongly on the stacking structures and selection of the layers. The Hall conductivity between different layers is no longer quantized. Moreover, for AB stacking, the interlayer conductivity vanishes around zero energy with increasing layer separation, and shows negative values in particular cases. The fact that longitudinal interlayer conductivity is suppressed by a magnetic field indicates that this system can be applied as a switching device.

DOI： 10.1103/PhysRevB.85.033403

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：WORLD SCIENTIFIC PUBL CO PTE LTD  

We discuss the metal-insulator transition of the spinless farm ion model with nearest-neighbor repulsion on the Kagome lattice at 1/3- and 2/3-filling. The system is analyzed by using exact diagonalization, the density-matrix renormalization group methods and the random phase approximation. In the strong-coupling region, the system is described by ring exchange processes. In the intermediate-coupling regime, we find that the qualitative properties of the metal-insulator transition at 1/3- and 2/3-filling are totally different reflecting the difference in the band structure near the Fermi level.

DOI： 10.1142/S0217984911026656

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

Fractional quantum Hall (FQH) states are topologically ordered which indicates that their essential properties are insensitive to smooth deformations of the manifold on which they are studied. Their microscopic Hamiltonian description, however, strongly depends on geometrical details. Recent work has shown how this dependence can be exploited to generate effective models that are both interesting in their own right and also provide further insight into the quantum Hall system. We review and expand on recent efforts to understand the FQH system close to the solvable thin-torus limit in terms of effective spin chains. In particular, we clarify how the difference between the bosonic and fermionic FQH states, which is not apparent in the thin-torus limit, can be seen at this level. Additionally, we discuss the relation of the Haldane-Shastry chain to the so-called QH circle limit and comment on its significance to recent entanglement studies. (C) 2010 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.physe.2010.07.044

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Language：English   Publishing type：Research paper (international conference proceedings)   Publisher：IOP PUBLISHING LTD  

We discuss the relationship between the fractional quantum Hall effect in the vicinity of the thin-torus, Tao-Thouless (TT), limit and quantum spin chains. We argue that the energetics of fractional quantum Hall states in Jain sequence at filling fraction v = p/(2p + 1) (and v = 1 p/(2p + 1)) in the lowest Landau level is captured by S = 1 spin chains with p spins in the unit cell. These spin chains naturally arise at sub-leading order in e(-2 pi 2)/L-1(2) which serves as an expansion parameter away from the TT limit (L-1 -&gt; 0). We also corroborate earlier results on the smooth Fermi surface deformation of the gapless state at; v = 1/2, interpolating between a state described by a critical S = 1/2 chain and the bulk.

DOI： 10.1088/1742-6596/302/1/012020

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We discuss the metal-insulator transition of the spinless fermion model on a kagome lattice at 1/3 filling. The system is analyzed by using exact diagonalization, density-matrix renormalization group methods, and random-phase approximation. In the strong-coupling region, the charge-ordered ground state is consistent with the predictions of an effective model, i.e., plaquette order. We find that the qualitative properties of the metal-insulator transition are totally different depending on the sign of the hopping matrix elements, reflecting the difference in the band structure near the Fermi level.

DOI： 10.1103/PhysRevLett.104.196401

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We study a strong coupling expansion of the nu = 1/3 fractional quantum Hall state away from the Tao-Thouless limit and show that the leading quantum fluctuations lead to an effective spin-1 Hamiltonian that lacks parity symmetry. By analyzing the energetics, discrete symmetries of low-lying excitations, and string order parameters, we demonstrate that the nu = 1/3 fractional quantum Hall state is adiabatically connected to both Haldane and large-D phases and is characterized by a string order parameter which is dual to the ordinary one. This result indicates a close relation between (a generalized form of) the Haldane conjecture for spin chains and the fractional quantum Hall effect.

DOI： 10.1103/PhysRevB.81.165102

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Physical properties reflecting the valley asymmetry of Landau levels in a biased bilayer graphene under a magnetic field are discussed. Within the 4-band continuum model with a Hartree-corrected self-consistent gap and finite damping factor we predict the appearance of anomalous steps in quantized Hall conductivity due to the degeneracy lifting of Landau levels. Moreover, the valley symmetry breaking effect appears as a nonsemiclassical de Haas-van Alphen effect where the reduction of the oscillation period to half cannot be accounted for through quasiclassical quantization of the orbits in reciprocal space.

DOI： 10.1103/PhysRevLett.103.266804

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We investigate the relation between the canonical model of quantum optics, the Jaynes-Cummings Hamiltonian and Dirac fermions in quantizing magnetic field. We demonstrate that Rabi oscillations are observable in the optical response of graphene, providing us with a transparent picture about the structure of optical transitions. While the longitudinal conductivity reveals chaotic Rabi oscillations, the Hall component measures coherent ones. This opens up the possibility of investigating a microscopic model of a few quantum objects in a macroscopic experiment with tunable parameters.

DOI： 10.1103/PhysRevLett.102.036803

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We discuss Hall effect of multilayer graphenes with several stacking structures (Bernal, rhombohedral and simple hexagonal) in strong- and weak-magnetic field regimes. For bilayer systems in strong-magnetic field region, we observed crossover of integer quantum Hall effect from two independent monolayer type system to strongly coupled bilayer systems by changing the ratio of interlayer hopping energy and the Fermi energy. In weak-magnetic field regime of few layer systems, Hall conductivity shows plateaux as functions of Fermi energy which reflects difference of stacking structures.

DOI： 10.1088/1742-6596/150/2/022064

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We discuss the quantum Hall effect of bilayer graphene with finite gate voltage where the Fermi energy exceeds the interlayer hopping energy. We calculated magnetic susceptibility, and diagonal and off-diagonal conductivities in finite-magnetic-field formalism. We also observed crossover of integer quantum Hall effect from two independent monolayer type systems to a strongly coupled bilayer system by changing the ratio of interlayer hopping energy and the Fermi energy. We also discuss the case of multilayer systems with Bernal stacking.

DOI： 10.1103/PhysRevB.78.033403

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We discuss electric transport and orbital magnetism of multilayer graphenes in a weak-magnetic field using the matrix decomposition technique. At zero temperature, the minimum conductivity is given by that of the monolayer system multiplied by the layer number N, independent of the interlayer hopping t. When the interlayer hopping satisfies the condition t τ with τ being collision time of impurity scattering, [N 2] kinks and [N 2] +1 plateaux appear in the Fermi-energy (gate voltage) dependence of the conductivity and the Hall conductivity, respectively. These behaviors are interpreted as multiband effects. We also found that the Hall conductivity and the magnetic susceptibility take minimum value as a function of temperature, for certain value of the gate voltage. This behavior is explained by Fermi-energy dependence of these functions at zero temperature. © 2008 The American Physical Society.

DOI： 10.1103/PhysRevB.77.045429

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We discuss electric transport and orbital magnetism of multilayer graphenes in a weak-magnetic field using the matrix decomposition technique. At zero temperature, the minimum conductivity is given by that of the monolayer system multiplied by the layer number N, independent of the interlayer hopping t. When the interlayer hopping satisfies the condition t &gt; h/tau with tau being collision time of impurity scattering, [N/2] kinks and [N/2]+1 plateaux appear in the Fermi-energy (gate voltage) dependence of the conductivity and the Hall conductivity, respectively. These behaviors are interpreted as multiband effects. We also found that the Hall conductivity and the magnetic susceptibility take minimum value as a function of temperature, for certain value of the gate voltage. This behavior is explained by Fermi-energy dependence of these functions at zero temperature.

DOI： 10.1103/PhysRevB.77.045429

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We discuss the orbital magnetism and the Hall effect in a weak magnetic field in two-dimensional Dirac fermion systems with an energy gap. This model is related to the graphene sheet, zero-gap organic conductors, and the d-density-wave state of cuprates. We found strong diamagnetism and anomalous Hall conductivity even in gapped systems. We also discuss the relation between results of the weak-magnetic-field formalism and those in a finite magnetic field with Landau quantization.

DOI： 10.1103/PhysRevB.76.113301

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

Two electron systems in one dimension, the quarter-filled extended Hubbard model with the alternating transfer integral and the half-filled ionic Hubbard model, are investigated. In both cases, their charge parts are expected to show the Ising criticality. We numerically determine the phase diagrams, and perform the finite-size scaling analysis of an excitation gap to show the evidence. Furthermore, we give the relationship between the twist operator and the Ising order parameter in a certain limit. (c) 2006 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.jmmm.2006.10.306

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We study superconductivity mediated by the charge fluctuation in two-dimensional organic conductor beta-(meso-DMBEDT-TTF)(2)PF6. We consider the extended Hubbard model on a weakly dimerized lattice, and solve the Eliashberg equations based on the random phase approximation. We found reentrant behavior of the checkerboard-type charge-ordered phase in the phase diagram, and the triplet superconductivity due to the charge fluctuation in the neighboring region. This results well agree with the experimental fact. (c) 2006 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.jmmm.2006.10.298

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We study theoretically competition between the charge ordering and the superconductivity in the two-dimensional organic conductor beta-(meso-DMBEDT-TTF)(2)PF6. We analyze the extended Hubbard model on a weakly-dimerized lattice based on the random phase approximation and Eliashberg equations. We found the reentrant behavior of the checkerbord-type charge-ordered phase in the phase diagram, and the triplet superconductivity due to the charge fluctuation in the neighboring region. In low temperatures, the singlet superconductivity also appears due to the enhancement of the spin fluctuation.

DOI： 10.1143/JPSJ.76.024706

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We study single-particle excitations of a Bose gas in an optical lattice in the Mott-insulator phase. The characteristic feature of the single-particle spectrum in the Mott-insulator phase is the existence of an energy gap between the particle and hole excitations. We show that the single-particle excitation energies and associated energy gap in the Mott-insulator phase can be directly probed by an output-coupling experiment. We apply the general expression for the output current derived by Luxat and Griffin, which is given in terms of the single-particle Green's functions of a trapped Bose gas, to the Mott-insulator phase using the Bose-Hubbard model. The energy spectrum of the momentum-resolved output current exhibits two characteristic peaks corresponding to the particle and hole excitations, and thus it can be used to detect the transition point from the Mott insulator to superfluid phase where the energy gap disappears.

DOI： 10.1103/PhysRevA.73.033621

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We study single-particle excitations of a Bose gas in an optical lattice in the Mott-insulator phase. The characteristic feature of the single-particle spectrum in the Mott-insulator phase is the existence of an energy gap between the particle and hole excitations. We show that the single-particle excitation energies and associated energy gap in the Mott-insulator phase can be directly probed by an output-coupling experiment. We apply the general expression for the output current derived by Luxat and Griffin, which is given in terms of the single-particle Green's functions of a trapped Bose gas, to the Mott-insulator phase using the Bose-Hubbard model. The energy spectrum of the momentum-resolved output current exhibits two characteristic peaks corresponding to the particle and hole excitations, and thus it can be used to detect the transition point from the Mott insulator to superfluid phase where the energy gap disappears. © 2006 The American Physical Society.

DOI： 10.1103/PhysRevA.73.033621

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We discuss the exact bond-ordered ground states of the one-dimensional half-filled generalized Hubbard model including three- and four-body terms, by decomposing the Hamiltonian into positive semidefinite parts. The obtained exact ground states are interpreted as Neel ordered states on the bond-located electrons. We determine parameter regions of the exact ground states. We also calculate elementary excitation energies as variational approach based on the matrix-product formalism.

DOI： 10.1103/PhysRevB.72.115121

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We study two one-dimensional electron systems, i.e., the quarter-filled extended Hubbard model with the alternating transfer integral and the half-filled ionic Hubbard model. In both cases, their charge parts are expected to show the two-dimensional Ising criticality as a resultant of two competing relevant perturbations on the Tomonaga-Luttinger liquid, and its description is given by the double-frequency sine-Gordon theory. Analyzing the excitation spectra of finite-size systems, we numerically determine the ground-state phase diagrams and check the theoretical predictions. (c) 2005 Elsevier B.V. All rights reserved.

DOI： 10.1016/j.physb.2005.01.439

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We investigate the ground-state phase diagram of the one-dimensional half-filled Hubbard model with an alternating potential-a model for the charge-transfer organic materials and the ferroelectric perovskites. We numerically determine the global phase diagram of this model using the level-crossing and the phenomenological renormalization-group methods based on the exact diagonalization calculations. Our results support the mechanism of the double phase transitions between Mott and band insulators pointed out by Fabrizio, Gogolin, and Nersesyan [Phys. Rev. Lett. 83, 2014 (1999)]: We confirm the existence of the spontaneously dimerized phase as an intermediate state. Further we provide numerical evidence to check the criticalities on the phase boundaries. Especially, we perform the finite-size-scaling analysis of the excitation gap to show the two-dimensional Ising transition in the charge part. On the other hand, we confirm that the dimerized phase survives in the strong-coupling limit, which is one of the resultants of competition between the ionicity and correlation effects.

DOI： 10.1103/PhysRevB.71.155105

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We show the existance of the exact plaquette-ordered ground states of the Hubbard model including site-off-diagonal interactions in arbitrary dimensions, by decomposing the Hamiltonian as sum of products of projection operators for each spin sector. The obtatined exact ground states are interpreted as Neel ordered states on the dual lattices. We demonstrate this idea in the one-dimensional chain and higher-dimensional lattices such as the Kagome lattice, and determine parameter regions of the exact ground states.

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We study the one-dimensional quarter-filled extended Hubbard model with an alternating transfer integral. In the strong-dimerization limit the charge part is described by the quantum Ising model which shows the two-dimensional Ising criticality at the self-dual point, and it is naturally connected to the double-frequency sine-Gordon theory in the weak dimerization. Treating low-lying excitations in finite-size systems, we numerically determine a phase boundary between two types of 4kF density-wave states and clarify the ground-state phase diagram. Further, we refer to its relevances to the charge-ordered phase observed in the charge-transfer organic salts.

DOI： 10.1103/PhysRevB.70.073105

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMERICAN PHYSICAL SOC  

We study the one-dimensional quarter-filled extended Hubbard model with an alternating transfer integral. In the strong-dimerization limit the charge part is described by the quantum Ising model which shows the two-dimensional Ising criticality at the self-dual point, and it is naturally connected to the double-frequency sine-Gordon theory in the weak dimerization. Treating low-lying excitations in finite-size systems, we numerically determine a phase boundary between two types of 4k(F) density-wave states and clarify the ground-state phase diagram. Further, we refer to its relevances to the charge-ordered phase observed in the charge-transfer organic salts.

DOI： 10.1103/PhysRevB.70.073105

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DOI： 10.1016/j.jmmm.2003.12.635

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We have proposed the plaquette-singlet solid (PSS) ground state for the spin-1 antiferromagnetic Heisenberg two-leg ladder. Based on the PSS picture, we discuss, the correspondence of the PSS state to the valence-bond solid (VBS) state of the ground state of spin-2 chain by introducing an appropriate composite spin picture. When the bond alternation is introduced, there occur quantum phase transitions and each phase can be identified with that in the dimerized spin-2 chain. Furthermore, we argue that the VBS picture of spin-2S chain can be applied to the ground state of spin-S two-leg ladder. (C) 2003 Elsevier Science B.V. All rights reserved.

DOI： 10.1016/S0921-4526(02)02190-7

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PHYSICAL SOC JAPAN  

We study phase transition between two topologically different gapped states in the spin-1/2 bond-alternating two-leg Heisenberg ladder by investigating string order parameters and the level-crossing method based on the exact diagonalization. We determine the phase diagram on the plane of the bond-alternation delta and the rung-leg coupling ratio J(perpendicular to)/J, and conclude that the boundary is given as J(perpendicular to)/J proportional to delta(2/3) in the weak coupling region J(perpendicular to)/J, delta much less than 1.

DOI： 10.1143/JPSJ.72.1022

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMERICAN PHYSICAL SOC  

We show that scalar chiral order can be induced by four-spin exchanges in the two-leg spin ladder, using the spin-chirality duality transformation and matrix-product ansatz. Scalar-chiral-ordered states are found to be exact ground states in a family of spin ladder models. In this scalar chiral phase, there is a finite energy gap above the doubly degenerate ground states and a Z(2)xZ(2)xZ(2) symmetry is fully broken. It is also shown that the SU(4)-symmetric model, which is self-dual under the duality transformation, is on a multicritical point surrounded by the staggered dimer phase, the staggered scalar chiral phase, and the gapless phase.

DOI： 10.1103/PhysRevB.67.174410

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：ELSEVIER SCIENCE BV  

We discuss relation between three different methods to identify topologically distinct short-range valence-bond ground states in spin-1/2 two-leg ladders: the string order parameters, the level-crossing method, and the ground-state 2 expectation value of the twist operator. For this purpose we reexamine a phase transition in the frustrated spin ladder. We propose a proper bosonization of the string order parameters. Then, these three methods are shown to be equivalent reflecting the Z(2) x Z(2) symmetry breaking of the order and the disorder fields of the two-dimensional Ising model. (C) 2003 Elsevier Science B.V. All rights reserved.

DOI： 10.1016/S0921-4526(02)02180-4

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Language：English   Publishing type：Research paper (scientific journal)  

DOI： 10.1103/PhysRevB.67.174410

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We propose an order parameter to characterize valence-bond-solid (VBS) states in quantum spin chains, given by the ground-state expectation value of a unitary operator appearing in the Lieb-Schultz-Mattis argument. We show that the order parameter changes the sign according to the number of valence bonds (broken valence bonds) at the boundary for periodic (open) systems. This allows us to determine the phase transition point in between different VBS states. We demonstrate this theory in the successive dimerization transitions of the bond-alternating Heisenberg chains, using the quantum Monte Carlo method.

DOI： 10.1103/PhysRevLett.89.077204

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

In one dimension, the exponential position operators introduced in a theory of polarization are identified with the twist operators appearing in the Lieb-Schultz-Mattis argument, and their finite-size expectation values z(L)((q)) measure the overlap between the q-fold degenerate ground state and an excited state. Insulators are characterized by z(infinity)not equal0, and different states are distinguished by the sign of z(L). We identify z(L) with ground-state expectation values of vertex operators in the sine-Gordon model. This allows an accurate detection of quantum phase transitions in the universality classes of the Gaussian and the SU(2)(1) Wess-Zumino-Novikov-Witten models. We apply this theory to the half-filled extended Hubbard model and obtain agreement with the level-crossing method.

DOI： 10.1103/PhysRevB.65.153110

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PROGRESS THEORETICAL PHYSICS PUBLICATION OFFICE  

We propose an order parameter to characterize valence-bond-solid (VBS) states in quantum spin systems, given by the ground-state expectation value of a unitary operator appearing in the Lieb-Schultz-Mattis argument. We show that the order parameter changes the sign according to the configuration of the valence bonds. This allows us to determine the phase transition point in between different VBS states accurately. We demonstrate this theory in the bond-alternating Heisenberg chain and in the frustrated spin ladder.

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PHYSICAL SOC JAPAN  

Phase diagram of the one-dimensional extended Hubbard model with a nearest neighbor interaction V and site-off-diagonal (bond-charge X and bond-bond W) interactions at half-filling is obtained analytically and numerically. For the numerical analysis, we used the level-crossing approach which has been applied to the W = 0 case [Phys. Rev. B 61 (2001) 16377]. Similarly to the X term, the W term enhances bond-charge-density-wave (BCDW) and bond-spin-density-wave (BSDW) phases for W &lt; 0 and W &gt; 0 cases, respectively. In addition we showed that an exact ground state corresponding to a BSDW state, and an eta -pairing ground state appear in this model.

DOI： 10.1143/JPSJ.70.3606

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PHYSICAL SOC JAPAN  

We Show the existence of all exact ground state in a parameter regime of a one-dimensional half-filled extended Hubbard model with site-off-diagonal interactions. In this ground state, the bond-located spin correlation exhibits a long-range order. In the case when the spin space is SU(2) symmetric, this ground state degenerates with higher spin states including a fully ferromagnetic state. We also discuss the relation between the exact bond-ordered ground state and the critical bond-spin-density-wave phase.

DOI： 10.1143/JPSJ.70.1202

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

Phase diagrams of the one-dimensional extended Hubbard model (including nearest-neighbor interaction V) at half- and quarter-filling are studied by observing level crossings of excitation spectra using the exact diagonalization. This method is based on the Tomonaga-Luttinger liquid theory including logarithmic corrections which stem from the renormalization of the Umklapp- and the backward-scattering effects. Using this approach, the phase boundaries are determined with high accuracy, and then the structure of the phase diagram is clarified. At half-filling, the phase diagram consists of two Berezinskii-Kosterlitz-Thouless (BKT) transition lines and one Gaussian transition line in the charge sector, and one spin-gap transition line. This structure reflects the U(1) x SU(2) symmetry of the electron system. Near the U = 2V line, the Gaussian and the spin-gap transitions take place independently from the weak- to the intermediate-coupling region, but these two transition lines are coupled in the strong-coupling region. This result demonstrates existence of a tricritical point and a bond-charge-density-wave (BCDW) phase between charge- and spin-density-wave (CDW, SDW) phases. To clarify this mechanism of the transition, we also investigate effect of a correlated hopping term, which plays a role to enlarge BCDW and bond-spin-density-wave (BSDW) phases. At quarter-filling, a similar crossover phenomenon also takes place in the large-V region involving spin-gap and BKT-type metal-insulator transitions.

DOI： 10.1103/PhysRevB.61.16377

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：PHYSICAL SOCIETY JAPAN  

The phase transition between charge- and spin-density-wave (CDW, SDW) phases is studied in the one-dimensional extended Hubbard model at half-filling. We discuss whether the transition can be described by Gaussian and spin-gap transitions under charge-spin separation, or by the direct CDW-SDW transition. These phase boundaries are determined by level crossings of excitation spectra which are identified according to discrete symmetries of wave functions. We conclude that the Gaussian and spin-gap transitions take place separately from the weak- to intermediate-coupling region, and a bond-order-wave phase exists between the CDW and the SDW states. Our results Are also consistent with those of the strong-coupling theory and of the direct evaluation of the CDW order parameters.

DOI： 10.1143/JPSJ.68.3123

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

We give details of the analysis of critical properties of spin-gap phases in one-dimensional lattice electron models. In Tomonaga-Luttinger (TL) liquid theory, the spin-gap instability occurs when the backward scattering changes from repulsive to attractive. This transition point is, shown to be equivalent to that of the level-crossing of the singlet and triplet excitation spectra, using the c=1 conformal field theory and the renormalization group. Based on this notion, the transition point between the TL liquid and the spin-gap phases can be determined with high-accuracy, from the numerical data of finite-size clusters. We also discuss the boundary conditions and discrete symmetries to extract these excitation spectra. This technique is applied to the extended Hubbard model, the t-J model, and the t-J-J' model, and their phase diagrams are obtained. We also discuss the relation between our results and analytical solutions in weak-coupling and low-density limits.

DOI： 10.1103/PhysRevB.60.7850

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Language：English   Publisher：PHYSICAL SOC JAPAN  

The spin-gap phase of the one-dimensional t-J-J' model is studied by the level-crossing of the singlet and the triplet excitation spectra. The phase boundary obtained between the Tomonaga-Luttinger and the spin-gap phases is remarkably consistent with the analytical results at the J, J' --&gt; 0 and the low-density limits discussed by Ogata et al. The spin-gap phase has a single domain in the phase diagram even if the spin gap opens at half-filling. The phase boundary coincides with the K-p = 1 line where the Tomonaga-Luttinger liquid behaves as free electrons, in the low-density region. The relation between our method and the solution of the two-electron problem is also discussed.

DOI： 10.1143/JPSJ.67.717

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMER PHYSICAL SOC  

Asymptotic behavior of the Tomonaga-Luttinger liquid in the vicinity of the phase-separated region is investigated in the one-dimensional t-J model to study the universal property of the c = 1 conformal field theory with U(1) symmetry near the K --&gt; infinity instability. By analogy to the spinless fermion, we argue that the compressibility behaves as kappa proportional to (J(c) - J)(-1), and that the Drude weight is constant and changes to zero discontinuously at the phase boundary. This speculation is confirmed by analyzing the finite-size effect from the result of the exact diagonalization.

DOI： 10.1103/PhysRevB.56.12840

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Language：English   Publishing type：Research paper (scientific journal)   Publisher：AMERICAN PHYSICAL SOC  

We study the spin-gap phase in the one-dimensional t-J model, assuming that it is caused by the backward scattering process. Based on the renormalization group analysis and symmetry, we can determine the transition point between the Tomonaga-Luttinger liquid and the spin-gap phases, by the level crossing of the singlet and the triplet excitations. In contrast to the previous works, the obtained spin-gap region is unexpectedly large. We also determine that the universality class of the transition belongs to the k = 1 SU(2) Wess-Zumino-Witten model.

DOI： 10.1103/PhysRevLett.79.3214

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Language：Japanese   Publisher：The Physical Society of Japan (JPS)  

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Language：Japanese   Publisher：物性研究刊行会  

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Other Link： http://hdl.handle.net/2433/97444

Language：Japanese   Publisher：物性研究刊行会  

量子スピン系のvalence bond solid (VBS)状態を特徴づける量として提案された、ひねり演算子の基底状態の期待値z_Lのスピン梯子系への応用を考える。また、string秩序変数やレベルクロスの方法との関連をZ_2×Z_2対称性の破れという観点から考察する。

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Other Link： http://dl.ndl.go.jp/info:ndljp/pid/10940322

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