arXiv subjects

Hosho Katsura

Publications and source records attributed to Hosho Katsura.

At least 109 records · Page 6Linked to original sources

arXiv2013

Ground-state Energies of Spinless Free Fermions and Hard-core Bosons

We compare the groundstate energies of bosons and fermions with the same form of the Hamiltonian. If both are noninteracting, the groundstate energy of bosons is always lower, owing to Bose-Einstein Condensation. However, the comparison is nontrivial when bosons do interact. We first prove that, when the hopping is unfrustrated (all the hopping amplitudes are non-negative), hard-core bosons still must have a lower groundstate energy than the fermions. When the hopping is frustrated, bosons can have higher groundstate energy than fermions. We prove rigorously that this inversion indeed occurs in several examples, using various techniques.

cond-mat.stat-mech↗

arXiv2013

Nagaoka states in the SU($n$) Hubbard model

We present an extension of Nagaoka's theorem in the SU($n$) generalization of the infinite-$U$ Hubbard model. It is shown that, when there is exactly one hole, the fully polarized states analogous to the ferromagnetic states in the SU(2) Hubbard model are ground states. For a restricted class of models satisfying the connectivity condition, these fully polarized states are the unique ground states up to the trivial degeneracy due to the SU($n$) symmetry. We also give examples of lattices in which the connectivity condition can be verified explicitly. The examples include the triangular, kagome, and hypercubic lattices in $d (\ge 2)$ dimensions, among which the cases of $d=2$ and 3 are experimentally realizable in ultracold atomic gases loaded into optical lattices.

cond-mat.str-el↗

arXiv2012

Ground States of the Spin-1 Bose-Hubbard Model

We prove basic theorems about the ground states of the S=1 Bose-Hubbard model. The results are quite universal and depend only on the coefficient U_2 of the spin-dependent interaction. We show that the ground state exhibits saturated ferromagnetism if U_2<0, is spin-singlet if U_2>0, and exhibits "SU(3)-ferromagnetism" if U_2=0, and completely determine the degeneracy in each region.

cond-mat.quant-gas↗

arXiv2012

Entanglement Spectra of the quantum hard-square model: Holographic minimal models

We study the entanglement properties of a quantum lattice-gas model for which we can find the exact ground state (of the Rokhsar-Kivelson type). The ground state can be expressed as a superposition of states, each of which is characterized by a particle configuration with nearest-neighbor exclusion. We show that the reduced density matrix of the model on a ladder is intimately related to the transfer matrix of the classical hard-square model. The entanglement spectra of the model on square and triangular ladders are critical when parameters are chosen so that the corresponding classical hard-square models are critical. A detailed analysis reveals that the critical theories for the entanglement Hamiltonians are $c<1$ minimal conformal field theories. We further show that the entanglement Hamiltonian for the triangular ladder is integrable despite the fact that the original quantum lattice-gas model is non-integrable.

cond-mat.stat-mech↗

arXiv2012

Theory of Raman Scattering in One-Dimensional Quantum Spin-1/2 Antiferromagnets

We study theoretically the Raman scattering spectra in the one-dimensional (1D) quantum spin-1/2 antiferromagnets. The analysis reveals that their low-energy dynamics is exquisitely sensitive to various perturbations to the Heisenberg chain with nearest-neighbor exchange interactions, such as magnetic anisotropy, longer-range exchange interactions, and bond dimerization. These weak interactions are mainly responsible for the Raman scattering and give rise to different types of spectra as functions of frequency, temperature, and external field. In contrast to the Raman spectra in higher dimensions in which the two-magnon process is dominant, those in 1D antiferromagnets provide much richer information on these perturbations.

cond-mat.str-el↗

arXiv2012

Interacting Fibonacci anyons in a Rydberg gas

A defining property of particles is their behavior under exchange. In two dimensions anyons can exist which, opposed to fermions and bosons, gain arbitrary relative phase factors or even undergo a change of their type. In the latter case one speaks of non-Abelian anyons - a particularly simple and aesthetic example of which are Fibonacci anyons. They have been studied in the context of fractional quantum Hall physics where they occur as quasiparticles in the $k=3$ Read-Rezayi state, which is conjectured to describe a fractional quantum Hall state at filling fraction $ν=12/5$. Here we show that the physics of interacting Fibonacci anyons can be studied with strongly interacting Rydberg atoms in a lattice, when due to the dipole blockade the simultaneous laser excitation of adjacent atoms is forbidden. The Hilbert space maps then directly on the fusion space of Fibonacci anyons and a proper tuning of the laser parameters renders the system into an interacting topological liquid of non-Abelian anyons. We discuss the low-energy properties of this system and show how to experimentally measure anyonic observables.

cond-mat.quant-gas↗

arXiv2012

Sine-square deformation of solvable spin chains and conformal field theories

We study solvable spin chains, one-dimensional massless Dirac fermions, and conformal field theories (CFTs) with sine-square deformation (SSD), in which the Hamiltonian density is modulated by the function $f(x)=\sin^2 (πx/\ell)$, where $x$ is the position and $\ell$ is the length of the system. For the XY chain and the transverse field Ising chain at criticality, it is shown that the ground state of an open system with SSD is identical to that of a uniform chain with periodic boundary conditions. The same holds for the massless Dirac fermions with SSD, corresponding to the continuum limit of the gapless XY chain. For general CFTs, we find that the Hamiltonian of a system with SSD has an expression in terms of the generators of the Virasoro algebra. This allows us to show that the vacuum state is an exact eigenstate of the sine-square deformed Hamiltonian. Furthermore, for a restricted class of CFTs associated with affine Lie (Kac-Moody) algebras, including $c=1$ Gaussian CFT, we prove that the vacuum is an exact ground state of the deformed Hamiltonian. This explains why the SSD has succeeded in suppressing boundary effects in one-dimensional critical systems, as observed in previous numerical studies.

cond-mat.stat-mech↗

arXiv2012

Entanglement Spectra of the 2D AKLT Model: VBS/CFT Correspondence

We investigate the entanglement properties of the valence-bond-solid (VBS) state defined on two-dimensional lattices, which is the exact ground state of the Affleck-Kennedy-Lieb-Tasaki model. It is shown that the entanglement entropy obeys an area law and the non-universal prefactor of the leading term is strictly less than $\ln 2$. The analysis of entanglement spectra for various lattices reveals that the reduced density matrix associated with the VBS state is closely related to a thermal density matrix of a {\it holographic} spin chain, whose spectrum is reminiscent of that of the spin-1/2 Heisenberg chain. This correspondence is further supported by comparing the entanglement entropy in the holographic spin chain with conformal field theory predictions.

cond-mat.str-el↗

arXiv2011

Sine-square deformation of free fermion systems in one and higher dimensions

We study free fermion systems with the sine-square deformation (SSD), in which the energy scale of local Hamiltonians is modified according to the scaling function f(x)=sin^2[π(x-1/2)/L], where x is the position of the local Hamiltonian and L is the length of the system in the x direction. It has been revealed that when applied to one-dimensional critical systems the SSD realizes the translationally-invariant ground state which is the same as that of the uniform periodic system. In this paper, we propose a simple theory to explain how the SSD maintains the translational invariance in the ground-state wave function. In particular, for a certain one-dimensional system with SSD, it is shown that the ground state is exactly identical with the Fermi sea of the uniform periodic chain. We also apply the SSD to two-dimensional systems and show that the SSD is able to suppress the boundary modulations from the open edges extremely well, demonstrating that the SSD works in any dimensions and in any directions.

cond-mat.stat-mech↗

arXiv2011

Notes on Inhomogeneous Quantum Walks

We study a class of discrete-time quantum walks with inhomogeneous coins defined in [Y. Shikano and H. Katsura, Phys. Rev. E {\bf 82}, 031122 (2010)]. We establish symmetry properties of the spectrum of the evolution operator, which resembles the Hofstadter butterfly.

quant-ph↗

arXiv2011

Nearly-flat bands with nontrivial topology

We report the theoretical discovery of a large class of 2D tight-binding models containing nearly-flat bands with nonzero Chern numbers. In contrast with previous studies, where nonlocal hoppings are usually required, the Hamiltonians of our models only require short-range hopping and have the potential to be realized in cold atomic gases. Due to the similarity with 2D continuum Landau levels, these topologically nontrivial nearly-flat bands may lead to the realization of fractional anomalous quantum Hall states and fractional topological insulators in real materials. Among the models we discover, the most interesting and practical one is a square-lattice three-band model which has only nearest-neighbor hopping. To understand better the physics underlying the topological flat band aspects, we also present the studies of a minimal two-band model on the checkerboard lattice.

cond-mat.str-el↗

arXiv2011

Exact ground state of the sine-square deformed XY spin chain

We study the sine-square deformed quantum XY chain with open boundary conditions, in which the interaction strength at the position $x$ in the chain of length $L$ is proportional to the function $f_x = \sin^2 [π/L (x-1/2)]$. The model can be mapped onto a free spinless fermion model with site-dependent hopping amplitudes and on-site potentials via the Jordan-Wigner transformation. Although the single-particle eigenstates of this system cannot be obtained in closed form, it is shown that the many-body ground state is identical to that of the uniform XY chain with periodic boundary conditions. This proves a conjecture of Hikihara and Nishino [Hikihara T and Nishino T 2011 {\it Phys. Rev. B} \textbf{83} 060414(R)] based on numerical evidence.

cond-mat.stat-mech↗

arXiv2011

Ferromagnetism in the Hubbard model with Topological/Non-Topological Flat Bands

We introduce and study two classes of Hubbard models with magnetic flux or with spin-orbit coupling, which have a flat lowest band separated from other bands by a nonzero gap. We study the Chern number of the flat bands, and find that it is zero for the first class but can be nontrivial in the second. We also prove that the introduction of on-site Coulomb repulsion leads to ferromagnetism in both the classes.

cond-mat.str-el↗

arXiv2011

General Relationship Between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States

We consider (2+1)-dimensional topological quantum states which possess edge states described by a chiral (1+1)-dimensional Conformal Field Theory (CFT), such as e.g. a general quantum Hall state. We demonstrate that for such states the reduced density matrix of a finite spatial region of the gapped topological state is a thermal density matrix of the chiral edge state CFT which would appear at the spatial boundary of that region. We obtain this result by applying a physical instantaneous cut to the gapped system, and by viewing the cutting process as a sudden "quantum quench" into a CFT, using the tools of boundary conformal field theory. We thus provide a demonstration of the observation made by Li and Haldane about the relationship between the entanglement spectrum and the spectrum of a physical edge state.

cond-mat.mes-hall↗

arXiv2010

Localization and Fractality in Inhomogeneous Quantum Walks with Self-Duality

We introduce and study a class of discrete-time quantum walks on a one-dimensional lattice. In contrast to the standard homogeneous quantum walks, coin operators are inhomogeneous and depend on their positions in this class of models. The models are shown to be self-dual with respect to the Fourier transform, which is analogous to the Aubry-André model describing the one-dimensional tight-binding model with a quasi-periodic potential. When the period of coin operators is incommensurate to the lattice spacing, we rigorously show that the limit distribution of the quantum walk is localized at the origin. We also numerically study the eigenvalues of the one-step time evolution operator and find the Hofstadter butterfly spectrum which indicates the fractal nature of this class of quantum walks.

quant-ph↗

arXiv2010

Theory of Thermal Hall Effect in Quantum Magnets

We present a theory of the thermal Hall effect in insulating quantum magnets, where the heat current is totally carried by charge-neutral objects such as magnons and spinons. Two distinct types of thermal Hall responses are identified. For ordered magnets, the intrinsic thermal Hall effect for magnons arises when certain conditions are satisfied for the lattice geometry and the underlying magnetic order. The other type is allowed in a spin liquid which is a novel quantum state since there is no order even at zero temperature. For this case, the deconfined spinons contribute to the thermal Hall response due to Lorentz force. These results offer a clear experimental method to prove the existence of the deconfined spinons via a thermal transport phenomenon.

cond-mat.str-el↗

arXiv2010

Extreme sensitivity of a frustrated quantum magnet: Cs_2CuCl_4

We report a thorough theoretical study of the low temperature phase diagram of Cs_2CuCl_4, a spatially anisotropic spin S=1/2 triangular lattice antiferromagnet, in a magnetic field. Our results, obtained in a quasi-one-dimensional limit in which the system is regarded as a set of weakly coupled Heisenberg chains, are in excellent agreement with experiment. The analysis reveals some surprising physics. First, we find that, when the magnetic field is oriented within the triangular layer, spins are actually most strongly correlated within planes perpendicular to the triangular layers. This is despite the fact that the inter-layer exchange coupling in Cs_2CuCl_4 is about an order of magnitude smaller than the weakest (diagonal) exchange in the triangular planes themselves. Second, the phase diagram in such orientations is exquisitely sensitive to tiny interactions, heretofore neglected, of order a few percent or less of the largest exchange couplings. These interactions, which we describe in detail, induce entirely new phases, and a novel commensurate-incommensurate transition, the signatures of which are identified in NMR experiments. We discuss the differences between the behavior of Cs_2CuCl_4 and an ideal two-dimensional triangular model, and in particular the occurrence of magnetization plateaux in the latter. These and other related results are presented here along with a thorough exposition of the theoretical methods, and a discussion of broader experimental consequences to Cs_2CuCl_4 and other materials.

cond-mat.str-el↗

arXiv2010

Continuous Matrix Product Ansatz for the One-Dimensional Bose Gas with Point Interaction

We study a matrix product representation of the Bethe ansatz state for the Lieb-Linger model describing the one-dimensional Bose gas with delta-function interaction. We first construct eigenstates of the discretized model in the form of matrix product states using the algebraic Bethe ansatz. Continuous matrix product states are then exactly obtained in the continuum limit with a finite number of particles. The factorizing $F$-matrices in the lattice model are indispensable for the continuous matrix product states and lead to a marked reduction from the original bosonic system with infinite degrees of freedom to the five-vertex model.

cond-mat.stat-mech↗