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Hosho Katsura

Publications and source records attributed to Hosho Katsura.

At least 73 records · Page 4Linked to original sources
arXiv2021

Rigorous results on the ground state of the attractive SU($N$) Hubbard model

We study the attractive SU($N$) Hubbard model with particle-hole symmetry. The model is defined on a bipartite lattice with the number of sites $N_A$ $(N_B)$ in the $A$ $(B)$ sublattice. We prove three theorems that allow us to identify the basic ground-state properties: the degeneracy, the fermion number, and the SU($N$) quantum number. We also show that the ground state exhibits charge density wave order when $|N_A-N_B|$ is macroscopically large. The theorems hold for a bipartite lattice in any dimension, even without translation invariance.

cond-mat.str-el↗
arXiv2020

${\mathbb Z}_2$ Topological Invariant for Magnon Spin Hall Systems

We propose a definition of a ${\mathbb Z}_2$ topological invariant for magnon spin Hall systems which are the bosonic analog of two-dimensional topological insulators in class AII. The existence of "Kramers pairs" in these systems is guaranteed by pseudo-time-reversal symmetry which is the same as time-reversal symmetry up to some unitary transformation. The ${\mathbb Z}_2$ index of each Kramers pair of bands is expressed in terms of the bosonic counterparts of the Berry connection and curvature. We construct explicit examples of magnon spin Hall systems and demonstrate that our ${\mathbb Z}_2$ index precisely characterizes the presence or absence of helical edge states. The proposed ${\mathbb Z}_2$ index and the formalism developed can be applied not only to magnonic systems but also to other non-interacting bosonic systems.

cond-mat.mes-hall↗
arXiv2020

Fate of fractional quantum Hall states in open quantum systems: characterization of correlated topological states for the full Liouvillian

Despite previous extensive analysis of open quantum systems described by the Lindblad equation, it is unclear whether correlated topological states, such as fractional quantum Hall states, are maintained even in the presence of the jump term. In this paper, we introduce the pseudo-spin Chern number of the Liouvillian which is computed by twisting the boundary conditions only for one of the subspaces of the doubled Hilbert space. The existence of such a topological invariant elucidates that the topological properties remain unchanged even in the presence of the jump term which does not close the gap of the effective non-Hermitian Hamiltonian (obtained by neglecting the jump term). In other words, the topological properties are encoded into an effective non-Hermitian Hamiltonian rather than the full Liouvillian. This is particularly useful when the jump term can be written as a strictly block-upper (-lower) triangular matrix in the doubled Hilbert space, in which case the presence or absence of the jump term does not affect the spectrum of the Liouvillian. With the pseudo-spin Chern number, we address the characterization of fractional quantum Hall states with two-body loss but without gain, elucidating that the topology of the non-Hermitian fractional quantum Hall states is preserved even in the presence of the jump term. This numerical result also supports the use of the non-Hermitian Hamiltonian which significantly reduces the numerical cost. Similar topological invariants can be extended to treat correlated topological states for other spatial dimensions and symmetry (e.g., one-dimensional open quantum systems with inversion symmetry), indicating the high versatility of our approach.

cond-mat.mes-hall↗
arXiv2020

Quantum Ising chain with boundary dephasing

We study the quantum Ising chain with boundary dephasing. By doubling the Hilbert space, the model is mapped to the Su-Schrieffer-Heeger model with imaginary chemical potential at the edges. We show analytically and numerically that the Liouvillian gap, i.e., the inverse relaxation time of the model, scales with the system size $ N $ as $ N^{-3} $.

cond-mat.stat-mech↗
arXiv2020

Ferromagnetism in the SU($n$) Hubbard model with a nearly flat band

We present rigorous results for the SU($n$) Fermi-Hubbard model on the railroad-trestle lattice. We first study the model with a flat band at the bottom of the single-particle spectrum and prove that the ground states exhibit SU($n$) ferromagnetism when the total fermion number is the same as the number of unit cells. We then perturb the model by adding extra hopping terms and make the flat band dispersive. Under the same filling condition, it is proved that the ground states of the perturbed model remain SU($n$) ferromagnetic when the bottom band is nearly flat. This is the first rigorous example of the ferromagnetism in nonsingular SU($n$) Hubbard models in which both the single-particle density of states and the on-site repulsive interaction are finite.

cond-mat.str-el↗
arXiv2019

Three-dimensional topological magnon systems

We propose a class of models for a magnonic analog of topological insulators in three dimensions. The models have pseudo-time-reversal symmetry which ensures the existence of bosonic Kramers pairs. We define a set of $\mathbb{Z}_2$ topological invariants that characterizes different topological phases and determines the presence or absence of surface Dirac cones. This is demonstrated by considering a bosonic counterpart of the Fu-Kane-Mele model on a diamond lattice. The model is found to exhibit three distinct phases analogous to strong topological, weak topological, and trivial insulator phases of the original fermionic model. We also discuss a possible realization of the thermal Hall effect of surface magnons in the presence of a magnetic field in proximity to a normal ferromagnet.

cond-mat.mes-hall↗
arXiv2019

Simulating quantum circuits by adiabatic computation: improved spectral gap bounds

Adiabatic quantum computing is a framework for quantum computing that is superficially very different to the standard circuit model. However, it can be shown that the two models are computationally equivalent. The key to the proof is a mapping of a quantum circuit to an an adiabatic evolution, and then showing that the minimum spectral gap of the adiabatic Hamiltonian is at least inverse polynomial in the number of computational steps $L$. In this paper we provide two simplified proofs that the gap is inverse polynomial. Both proofs result in the same lower bound for the minimum gap, which for $L \gg 1$ is $\min_sΔ\gtrsim π^2 / [8(L+1)^2]$, an improvement over previous estimates. Our first method is a direct approach based on an eigenstate ansatz, while the the second uses Weyl's theorem to leverage known exact results into a bound for the gap. Our results suggest that it may be possible to use these methods to find bounds for spectral gaps of Hamiltonians in other scenarios.

quant-ph↗
arXiv2019

Transforming Generalized Ising Model into Boltzmann Machine

We find an exact mapping from the generalized Ising models with many-spin interactions to equivalent Boltzmann machines, i.e., the models with only two-spin interactions between physical and auxiliary binary variables accompanied by local external fields. More precisely, the appropriate combination of the algebraic transformations, namely the star-triangle and decoration-iteration transformations, allows one to express the model in terms of fewer-spin interactions at the expense of the degrees of freedom. Furthermore, the benefit of the mapping in Monte Carlo simulations is discussed. In particular, we demonstrate that the application of the method in conjunction with the Swendsen-Wang algorithm drastically reduces the critical slowing down in a model with two- and three-spin interactions on the Kagomé lattice.

cond-mat.stat-mech↗
arXiv2019

Supersymmetry Breaking and Nambu-Goldstone Fermions in Interacting Majorana Chains

We introduce and study a lattice fermion model in one dimension with explicit $\mathcal{N}=1$ supersymmetry (SUSY). The Hamiltonian of the model is defined by the square of a supercharge built from Majorana fermion operators. The model describes interacting Majorana fermions and its properties depend only on a single parameter $g$. When $g=1$, we find that SUSY is unbroken and the ground states are identical to those of the frustration-free Kitaev chains. We also find a parameter regime in which SUSY is restored in the infinite volume limit. For sufficiently large $g$, we prove that SUSY is spontaneously broken and the low-lying excitations are gapless, which can be thought of as Nambu-Goldstone fermions. We then show numerically that these gapless modes have cubic dispersion at long wavelength.

cond-mat.str-el↗
arXiv2019

Rigorous Results for the Ground States of the Spin-2 Bose-Hubbard Model

We present rigorous and universal results for the ground states of the $f=2$ spinor Bose-Hubbard model. The model includes three two-body on site interaction terms, two of which are spin dependent while the other one is spin independent. We prove that, depending only on the coefficients of the two spin dependent terms, the ground state exhibits maximum or minimum total spin or SU(5) ferromagnetism. Exact ground-state degeneracies and the forms of ground-state wave function are also determined in each case. All these results are valid regardless of dimension, lattice structure, or particle number. Our approach takes advantage of the symmetry of the Hamiltonian and employs mathematical tools including the Perron-Frobenius theorem and the Lie algebra $\mathfrak{so}(5)$.

cond-mat.quant-gas↗
arXiv2018

Effective dimension, level statistics, and integrability of Sachdev-Ye-Kitaev-like models

The Sachdev-Ye-Kitaev (SYK) model attracts attention in the context of information scrambling, which represents delocalization of quantum information and is quantified by the out-of-time-ordered correlators (OTOC). The SYK model contains $N$ fermions with disordered and four-body interactions. Here, we introduce a variant of the SYK model, which we refer to as the Wishart SYK model. We investigate the Wishart SYK model for complex fermions and that for hard-core bosons. We show that the ground state of the Wishart SYK model is massively degenerate and the residual entropy is extensive, and that the Wishart SYK model for complex fermions is integrable. In addition, we numerically investigate the OTOC and level statistics of the SYK models. At late times, the OTOC of the fermionic Wishart SYK model exhibits large temporal fluctuations, in contrast with smooth scrambling in the original SYK model. We argue that the large temporal fluctuations of the OTOC are a consequence of a small effective dimension of the initial state. We also show that the level statistics of the fermionic Wishart SYK model is in agreement with the Poisson distribution, while the bosonic Wishart SYK model obeys the GUE or the GOE distribution.

cond-mat.stat-mech↗
arXiv2018

Parity-time-symmetric topological superconductor

We investigate a topological superconducting wire with balanced gain and loss that is effectively described by the non-Hermitian Kitaev/Majorana chain with parity-time symmetry. This system is shown to possess two distinct types of unconventional edge modes, those with complex energies and nonorthogonal Majorana zero modes. The latter edge modes cause nonlocal particle transport with currents that are localized at the edges and absent in the bulk. This anomalous particle transport results from the interplay between parity-time symmetry (non-Hermiticity) and topological superconductivity.

cond-mat.mes-hall↗
arXiv2018

The Noncommutative Index Theorem and the Periodic Table for Disordered Topological Insulators and Superconductors

We study a wide class of topological free-fermion systems on a hypercubic lattice in spatial dimensions $d\ge 1$. When the Fermi level lies in a spectral gap or a mobility gap, the topological properties, e.g., the integral quantization of the topological invariant, are protected by certain symmetries of the Hamiltonian against disorder. This generic feature is characterized by a generalized index theorem which is a noncommutative analogue of the Atiyah-Singer index theorem. The noncommutative index defined in terms of a pair of projections gives a precise formula for the topological invariant in each symmetry class in any dimension ($d \ge 1$). Under the assumption on the nonvanishing spectral or mobility gap, we prove that the index formula reproduces Bott periodicity and all of the possible values of topological invariants in the classification table of topological insulators and superconductors. We also prove that the indices are robust against perturbations that do not break the symmetry of the unperturbed Hamiltonian.

math-ph↗
arXiv2018

Learning Disordered Topological Phases by Statistical Recovery of Symmetry

In this letter, we apply the artificial neural network in a supervised manner to map out the quantum phase diagram of disordered topological superconductor in class DIII. Given the disorder that keeps the discrete symmetries of the ensemble as a whole, translational symmetry which is broken in the quasiparticle distribution individually is recovered statistically by taking an ensemble average. By using this, we classify the phases by the artificial neural network that learned the quasiparticle distribution in the clean limit, and show that the result is totally consistent with the calculation by the transfer matrix method or noncommutative geometry approach. If all three phases, namely the $\mathbb{Z}_2$, trivial, and the thermal metal phases appear in the clean limit, the machine can classify them with high confidence over the entire phase diagram. If only the former two phases are present, we find that the machine remains confused in the certain region, leading us to conclude the detection of the unknown phase which is eventually identified as the thermal metal phase. In our method, only the first moment of the quasiparticle distribution is used for input, but application to a wider variety of systems is expected by the inclusion of higher moments.

cond-mat.dis-nn↗
arXiv2018

Mechanism for subgap optical conductivity in honeycomb Kitaev materials

Motivated by recent terahertz absorption measurements in $α$-RuCl$_3$, we develop a theory for the electromagnetic absorption of materials described by the Kitaev model on the honeycomb lattice. We derive a mechanism for the polarization operator at second order in the nearest-neighbor hopping Hamiltonian. Using the exact results of the Kitaev honeycomb model, we then calculate the polarization dynamical correlation function corresponding to electric dipole transitions, in addition to the spin dynamical correlation function corresponding to magnetic dipole transitions.

cond-mat.str-el↗
arXiv2018

Particle Statistics, Frustration, and Ground-State Energy

We study the connections among particle statistics, frustration, and ground-state energy in quantum many-particle systems. In the absence of interaction, the influence of particle statistics on the ground-state energy is trivial: the ground-state energy of noninteracting bosons is lower than that of free fermions because of Bose-Einstein condensation and Pauli exclusion principle. In the presence of hard-core or other interaction, however, the comparison is not trivial. Nevertheless, the ground-state energy of hard-core bosons is proved to be lower than that of spinless fermions, if all the hopping amplitudes are nonnegative. The condition can be understood as the absence of frustration among hoppings. By mapping the many-body Hamiltonian to a tight-binding model on a fictitious lattice, we show that the Fermi statistics of the original particles introduces an effective magnetic flux in the fictitious lattice. The latter can be regarded as a frustration, since it leads to a destructive interference among different paths along which a single particle is propagating. If we introduce hopping frustration, the hopping frustration is expected to compete with "effective frustration", leading to the possibility that the ground-state energy of hard-core bosons can be higher than that of fermions. We present several examples, in which the ground-state energy of hard-core bosons is proved to be higher than that of fermions due to the hopping frustration. The basic ideas were reported in a recent Letter [W.-X. Nie, H. Katsura, and M. Oshikawa, Phys. Rev. Lett. 111, 100402 (2013)]; more details and several extensions, including one to the spinful case, are discussed in the present paper.

cond-mat.stat-mech↗
arXiv2017

Proposal of a spin-one chain model with competing dimer and trimer interactions

A new kind of spin-1 chain Hamiltonian consisting of competing dimer and trimer projection operators is proposed. As the relative strengths and signs of the interactions are varied, the model exhibits a number of different phases including the gapped dimer phase and the gapless trimer phase with critical correlations described by a conformal field theory with central charge $c=2$. A symmetry-protected topological phase also exists in this model, even though the microscopic interactions are not the simple adiabatic extensions of the well-known Heisenberg and the Affleck-Kennedy-Lieb-Tasaki model and contains both two- and three-particle permutations. A fourth phase is characterized by macroscopically degenerate ground states. While bearing almost a one-to-one resemblance to the phase diagram of the bilinear-biquadratic spin-1 chain Hamiltonian, our model is rooted on very different physical origin, namely the two competing tendencies of spin-1 particles to form singlets through either dimer or trimer formation.

cond-mat.str-el↗