arXiv subjects

Nobuyuki Okuma

Publications and source records attributed to Nobuyuki Okuma.

At least 19 recordsLinked to original sources

arXiv2026

Divergent Orbital Diamagnetism from Chiral Edge States in Chern Insulators

Two-dimensional massless Dirac systems, exemplified by graphene, are known to exhibit a divergent orbital diamagnetic susceptibility that scales linearly with system size. Motivated by viewing a chiral edge state as one half of an enlarged analogue of a benzene ring, we study Chern insulators under open boundary conditions and find the same divergent scaling. This giant diamagnetism is robust against disorder, revealing its topological nature. Our results further suggest a profound connection to the divergent diamagnetism of massless Dirac systems.

cond-mat.mes-hall↗

arXiv2026

Predicting quantum ground-state energy by data-driven Koopman analysis of variational parameter nonlinear dynamics

In recent years, the application of machine learning to physics has been actively explored. In this paper, we study a method for estimating the ground-state energy of quantum Hamiltonians by applying data-driven Koopman analysis within the framework of variational wave functions. Koopman theory is a framework for analyzing the nonlinear dynamics of vectors, in which the dynamics are linearized by lifting the vectors to functions defined over the original vector space. We focus on the fact that the imaginary-time Schrödinger equation, when restricted to a variational wave function, is described by a nonlinear time evolution of the variational parameter vector. We collect sample points of this nonlinear dynamics at parameter configurations where the discrepancy between the true imaginary-time dynamics and the dynamics on the variational manifold is small, and perform data-driven continuous Koopman analysis. Within our formulation, the ground-state energy is reduced to the leading eigenvalue of a differential operator known as the Koopman generator. As a concrete example, we generate samples for the four-site transverse-field Ising model and estimate the ground-state energy using extended dynamic mode decomposition (EDMD). Furthermore, as an extension of this framework, we formulate the method for the case where the variational wave function is given by a uniform matrix product state on an infinite chain. By employing computational techniques developed within the framework of the time-dependent variational principle, all the quantities required for our analysis, including error estimation, can be computed efficiently in such systems. Since our approach provides predictions for the ground-state energy even when the true ground state lies outside the variational manifold, it is expected to complement conventional variational methods.

cond-mat.str-el↗

arXiv2026

Localized-basis formulation of interacting Hamiltonians in flat topological bands: coherent states and coherent-like states for fractional physics

In topological bands, it is impossible to construct exponentially localized Wannier functions while preserving the symmetries. Instead, in quantum Hall systems, one can define an overcomplete basis of spatially localized coherent states. In this work, we propose a unified framework for understanding the quantum Hall effect and Chern insulators from the perspective of localized bases, by extending the overcomplete basis of coherent states to Chern bands in terms of coherent-like states. Specifically, by representing both coherent states and coherent-like states as wave packets defined on a band, the difference between them can be encoded solely in the functional form of the wave packet in momentum space. Furthermore, for filling factor $ν=1/3$, we define a local repulsive interaction Hamiltonian based on these bases and discuss properties of its ground states. In particular, by relating this Hamiltonian to previously studied models, we show that in quantum Hall systems it possesses exactly zero-energy ground states with topological degeneracy, thereby confirming that it serves as a model for fractional quantum Hall systems. In addition, we numerically verify that the Hamiltonian possesses topological degeneracy for representative Chern insulator models. An advantage of this formulation is that it allows fractional quantum Hall systems and various fractional Chern insulator systems to be discussed within a unified framework using the same Hamiltonian form. In addition, we discuss that coherent-like states can also be defined in $\mathbb{Z}_2$ topological insulators. Corresponding to the fermionic time-reversal symmetry of the system, Kramers-degenerate coherent-like states can be naturally defined. The localized basis constructed from coherent-like states is expected to be useful for describing strongly correlated topological phases in flat-band systems.

cond-mat.str-el↗

arXiv2026

Steady-state skin effect in bosonic topological edge states under parametric driving

Non-Hermitian systems have attracted significant theoretical interest due to their extreme properties. However, realizations have mostly been limited to classical applications or artificial setups. In this study, we focus on the quantum nature inherent in bosonic Bogoliubov-de Gennes (BdG) systems, which from the perspective of spectral theory corresponds to non-Hermiticity. Based on this insight, we propose a steady-state skin effect in quantum condensed matter utilizing such BdG non-Hermiticity. Specifically, we introduce BdG quantum terms arising from parametric pumping to the edge states of an underlying bosonic Hermitian Chern insulator, thereby realizing non-Hermiticity without dissipation. This system design has the advantage of being largely independent of microscopic model details. Through analysis using non-equilibrium Green's functions, we find that under open boundary conditions, a steady state exhibiting the non-Hermitian skin effect is realized. The pronounced corner particle accumulation observed in this steady state shows quadrature anisotropy, which manifests the bosonic quantum nature. Our results bridge the gap between the fascinating mathematics of non-Hermitian matrices and practical quantum physical systems.

cond-mat.mes-hall↗

arXiv2026

Non-Hermitian topological superconductivity with symmetry-enriched spectral and eigenstate features

We investigate a one-dimensional superconducting lattice that realizes all internal symmetries permitted in non-Hermitian systems, characterized by nonreciprocal hopping, onsite dissipation, and $s$-wave singlet pairing in a Su-Schrieffer-Heeger-type structure. The combined presence of pseudo-Hermiticity and sublattice symmetry imposes constraints on the energy spectra. We identify parameter regimes featuring real spectra, purely imaginary spectra, complex flat bands, and Majorana zero modes, the latter emerging when a uniform transverse magnetic field suppresses the non-Hermitian skin effect. We show that a uniform onsite dissipation is essential for stabilizing the zero modes, whereas a purely staggered dissipation destroys the topological superconductivity. Through Hermitianization, we construct a spectral winding number as a topological invariant and demonstrate its correspondence with the gap closing conditions and appearance of the Majorana zero modes, allowing us to establish topological phase diagrams. Moreover, we reveal nontrivial correlations between the particle-hole and spin components of left and right eigenstates, enforced by chiral symmetry, pseudo-Hermiticity, and their combination. Our results highlight how non-Hermiticity, sublattice structure, and superconductivity together enrich symmetry properties and give rise to novel topological phenomena.

cond-mat.mes-hall↗

arXiv2025

Topological two-body interaction obstructing trivial ground states: an indicator of fractional Chern insulators

The search for candidate materials for fractional Chern insulators (FCIs) has mainly focused on the topological and geometrical structures of single-particle Chern bands. However, there are inherent limitations in approaches that neglect interaction effects, highlighting the need for complementary methods. In this work, we discuss how the Chern number defined for the effective interaction projected onto a Chern band is related to the stabilization of FCIs. Specifically, by formulating both the effective interaction and the two-particle problem using a common matrix, we establish a connection between the two-particle band structure and the effective interaction. This formulation allows us to characterize the effective interaction through the topology of the two-particle band. To investigate the relationship between topological effective interactions and FCIs, we perform numerical calculations primarily based on exact diagonalization. We find a notable correlation between the fact that the dominant two-particle bands carry a unit Chern number and the realization of a robust FCI at the filling fraction $ν= 1/3$. This result is consistent with the presumed correspondence between pseudopotentials in the fractional quantum Hall effect and the two-particle band structure. From another perspective, our findings suggest that the topology inherent in the interaction itself can obstruct trivial ground states. We also discuss this in the context of scattering channels. Extending such topological two-body interactions could pave the way for realizing exotic states beyond FCIs.

cond-mat.str-el↗

arXiv2025

Biorthogonal basis approach to fractional Chern physics

A fractional Chern insulator is thought to emerge from the competition between one-particle band topology and strong repulsive interactions. As an attempt to study lattice models of fractional Chern insulators, we introduce a biorthogonal basis constructed from coherent-like states on the von Neumann lattice. Focusing on the fact that this basis is diagonal to the vortex attachment in the infinite-volume limit, we convert the original fermions into composite fermions by applying a two-dimensional Jordan-Wigner transformation to the creation and annihilation operators of the biorthogonal basis. Furthermore, we apply the Hartree-Fock mean-field approximation to handle the interaction Hamiltonian of composite fermions. Due to the biorthogonal nature, the representation of the new Hamiltonian is no longer Hermitian, which implies that the introduction of the approximation does not guarantee the reality of the energy spectrum. In fact, there are many self-consistent solutions with complex spectra. Nevertheless, we numerically find that it is possible to construct a self-consistent solution where the band dispersion is nearly real and the ground-state energy is lower than in other solutions.

cond-mat.str-el↗

arXiv2025

Constructing vortex functions and basis states of Chern insulators: ideal condition, inequality from index theorem, and coherent-like states on von Neumann lattice

In the field of fractional Chern insulators, a great deal of effort has been devoted to characterizing Chern bands that exhibit properties similar to the Landau levels. Among them, the concept of the vortex function, which generalizes the complex coordinate used for the symmetric-gauge Landau-level basis, allows for a concise description. In this paper, we develop a theory of constructing the vortex function and basis states of Chern insulators in the tight-binding formalism. In the first half, we consider the optimization process of the vortex function, which minimizes an indicator that measures the difference from the ideal Chern insulators. In particular, we focus on the sublattice position dependence of the vortex function or the quantum geometric tensor. This degree of freedom serves as a discrete analog of the non-uniformity in the spatial metric and magnetic field in a continuous model. In the second half, we construct two types of basis sets for a given vortex function: radially localized basis set and coherent-like basis set. The former basis set is defined as the eigenstates of an analogy of the angular momentum operator. Remarkably, one can always find exact zero mode(s) for this operator, which is explained by the celebrated Atiyah-Singer index theorem. As a byproduct, we propose an inequality rooted in the band topology. We also discuss the subtle differences between our formalism and the previous works about the momentum-space Landau level. The latter basis set generalizes the concept of coherent states on von Neumann lattice. While this basis set is not orthogonal, it is useful to compare the LLL and the given Chern insulator directly in the Brillouin zone. These basis sets are expected to be useful for many-body calculations of fractional Chern insulators.

cond-mat.mes-hall↗

arXiv2024

Universal platform of point-gap topological phases from topological materials

Whereas point-gap topological phases are responsible for exceptional phenomena intrinsic to non-Hermitian systems, their realization in quantum materials is still elusive. Here we propose a simple and universal platform of point-gap topological phases constructed from Hermitian topological insulators and superconductors. We show that (d-1)-dimensional point-gap topological phases are realized by making a boundary in d-dimensional topological insulators and superconductors dissipative. A crucial observation of the proposal is that adding a decay constant to boundary modes in d-dimensional topological insulators and superconductors is topologically equivalent to attaching a (d-1)-dimensional point-gap topological phase to the boundary. We furthermore establish the proposal from the extended version of the Nielsen-Ninomiya theorem, relating dissipative gapless modes to point-gap topological numbers. From the bulk-boundary correspondence of the point-gap topological phases, the resultant point-gap topological phases exhibit exceptional boundary states or in-gap higher-order non-Hermitian skin effects.

cond-mat.mes-hall↗

arXiv2024

On equivalence of two formulas of orbital magnetic susceptibility for tight-binding models

We prove that two formulas of the orbital magnetic susceptibility, namely, Koshino-Ando's formula and Gómez-Santos and Stauber's formula, are equivalent for the tight-binding models. The difference between these two formulas can be written in a form containing the surface terms arising from the momentum-space integration, and we show that the surface terms are exactly vanishing although the primitive functions are seemingly non-periodic with respect to the translation by the reciprocal lattice vector.

cond-mat.mes-hall↗

arXiv2024

Topological enhancement of non-normality in non-Hermitian skin effects

The non-Hermitian skin effects are representative phenomena intrinsic to non-Hermitian systems: the energy spectra and eigenstates under the open boundary condition (OBC) drastically differ from those under the periodic boundary condition (PBC). Whereas a non-trivial topology under the PBC characterizes the non-Hermitian skin effects, their proper measure under the OBC has not been clarified yet. This paper reveals that topological enhancement of non-normality under the OBC accurately quantifies the non-Hermitian skin effects. Correspondingly to spectrum and state changes of the skin effects, we introduce two scalar measures of non-normality and argue that the non-Hermitian skin effects enhance both macroscopically under the OBC. We also show that the enhanced non-normality correctly describes phase transitions causing the non-Hermitian skin effects and reveals the absence of non-Hermitian skin effects protected by average symmetry. The topological enhancement of non-normality governs the perturbation sensitivity of the OBC spectra and the anomalous time-evolution dynamics through the Bauer-Fike theorem.

cond-mat.mes-hall↗

arXiv2023

Bosonic Andreev bound state

A general free bosonic system with a pairing term is described by a bosonic Bogoliubov-de Gennes (BdG) Hamiltonian. The representation is given by a pseudo-Hermitian matrix, which is crucially different from the Hermitian representation of a fermionic BdG Hamiltonian. In fermionic BdG systems, a topological invariant of the whole particle (hole) bands can be nontrivial, which characterizes the Andreev bound states (ABS) including Majorana fermions. In bosonic cases, on the other hand, the corresponding topological invariant is thought to be trivial owing to the stability condition of the bosonic ground state. In this Letter, we consider a two-dimensional model that realizes a bosonic analogy of the ABS. The boundary states of this model are located outside the bulk bands and are characterized by a nontrivial Berry phase (or polarization) of the hole band. Furthermore, we investigate the zero-energy flat-band limit in which the Bloch Hamiltonian is defective, where the particle and hole states are identical to each other. In this limit, the Berry phase is $\mathbb{Z}_2$ quantized thanks to an emergent parity-time symmetry. This is an example of a topological invariant that uses the defective nature as a projection structure. Thus, boundary states in our model are essentially different from Hermitian topological modes and their variants.

cond-mat.mes-hall↗

arXiv2022

Relationship between two-particle topology and fractional Chern insulator

Lattice generalizations of fractional quantum Hall (FQH) systems, called fractional Chern insulators (FCIs), have been extensively investigated in strongly correlated systems. Despite many efforts, previous studies have not revealed all of the guiding principles for the FCI search. In this paper, we investigate a relationship between the topological band structure in the two-particle problem and the FCI ground states in the many-body problem. We first formulate the two-particle problem of a bosonic on-site interaction projected onto the lowest band of a given tight-binding Hamiltonian. We introduce a reduced Hamiltonian whose eigenvalues correspond to the two-particle bound-state energies. By using the reduced Hamiltonian, we define the two-particle Chern number and numerically check the bulk-boundary correspondence that is predicted by the two-particle Chern number. We then propose that a nontrivial two-particle Chern number of dominant bands roughly indicates the presence of bosonic FCI ground states at filling factor $ν=1/2$. We numerically investigate this relationship in several tight-binding models with Chern bands and find that it holds well in most of the cases, albeit two-band models being exceptions. Although the two-particle topology is neither a necessary nor a sufficient condition for the FCI state as other indicators in previous studies, our numerical results indicate that the two-particle topology characterizes the degree of similarity to the FQH systems.

cond-mat.str-el↗

arXiv2022

Non-Hermitian topological phenomena: A review

The past decades have witnessed an explosion of interest in topological materials, and a lot of mathematical concepts have been introduced in condensed matter physics. Among them, the bulk-boundary correspondence is the central topic in topological physics, which has inspired researchers to focus on boundary physics. Recently, the concepts of topological phases have been extended to non-Hermitian Hamiltonians, whose eigenvalues can be complex. Besides the topology, non-Hermiticity can also cause a boundary phenomenon called the non-Hermitian skin effect, which is an extreme sensitivity of the spectrum to the boundary condition. In this article, we review developments in non-Hermitian topological physics by focusing mainly on the boundary problem. As well as the competition between non-Hermitian and topological boundary phenomena, we discuss the topological nature inherent in non-Hermiticity itself.

cond-mat.mes-hall↗

arXiv2022

Boundary-dependent dynamical instability of bosonic Green's function: Dissipative Bogoliubov-de Gennes Hamiltonian and its application to non-Hermitian skin effect

The energy spectrum of bosonic excitations from a condensate is given by the spectrum of a non-Hermitian Hamiltonian constructed from a bosonic Bogoliubov-de Gennes (BdG) Hamiltonian in general even though the system is essentially Hermitian. In other words, two types of non-Hermiticity can coexist: one from the bosonic BdG nature and the other from the open quantum nature. In this paper, we propose boundary-dependent dynamical instability. We first define the bosonic dissipative BdG Hamiltonian in terms of Green's function in Nambu space and discuss the correct particle-hole symmetry of the corresponding non-Hermitian Hamiltonian. We then construct a model of the boundary-dependent dynamical instability so that it satisfies the correct particle-hole symmetry. In this model, an anomalous term that breaks the particle number conservation represents the non-Hermiticity of the BdG nature, while a normal term is given by a dissipative Hatano-Nelson model. Thanks to the competition between the two types of non-Hermiticity, the imaginary part of the spectrum can be positive without the help of the amplification of the normal part and the particle-hole band touching that causes the Landau instability. This leads to the boundary-dependent dynamical instability under the non-Hermitian skin effect, -strong dependence of spectra on boundary conditions for non-Hermitian Hamiltonians-, of the Bogoliubov spectrum.

cond-mat.mes-hall↗

arXiv2021

Time-crystalline long-range order in chiral fermionic vacuum

It is widely believed that there is no macroscopic time-crystalline order in the ground states of short-range interacting systems. In this paper, we consider a time-dependent correlation function for an order operator with a spatially discontinuous weight in a one-dimensional chiral fermionic system. Although both the Hamiltonian and the order parameter are composed of spatially local operators, the time-dependent correlation function diverges logarithmically in equal time intervals. This result implies a breakdown of an inequality that claims the absence of time-crystalline long-range order in the ground states, unless the upper-bound constant is set to be infinity. This behavior is due to the combination of the discontinuity of the order operator and the infinite dimensionality of quantum field theory. In the language of bosonization, it can also be related to the divergence of a space-time-resolved bosonic correlation function.

cond-mat.mes-hall↗

arXiv2021

Time-crystalline long-range order in squeezed ground state

It is widely believed that ground-state time crystals are not realizable in realistic macroscopic systems. In particular, Watanabe and Oshikawa proved a theorem that implies the absence of the time-dependent long-range order (TDLRO) in the ground states of short-range many-body systems. However, this theorem does not forbid the presence of the ground-state TDLRO for macroscopic quantities. In this work, we investigate a simple bosonic model with a squeezed ground state and point out that the time-dependence of the ground-state TDLRO for the number operator is proportional to the square of the average number in the infinite-squeezing limit, or equivalently, the infinite average-number limit. This result implies the presence of the TDLRO for macroscopic boson number. We also discuss the physical implementations in optical, spin, and tight-binding systems, including the variants. We find an example with the macroscopic TDLRO whose essence is low-lying-state physics and another with $marginal$ TDLRO at the quantum critical point. In addition, we reconsider the definition of the ground-state time crystal in terms of the Floquet picture.

cond-mat.mes-hall↗

arXiv2021

Non-normal Hamiltonian dynamics in quantum systems and its realization on quantum computers

The eigenspectrum of a non-normal matrix, which does not commute with its Hermitian conjugate, is a central issue of non-Hermitian physics that has been extensively studied in the past few years. There is, however, another characteristic of a non-normal matrix that has often been overlooked: the pseudospectrum, or the set of spectra under small perturbations. In this paper, we study the dynamics driven by the non-normal matrix (Hamiltonian) realized as a continuous quantum trajectory of the Lindblad master equation in open quantum systems and point out that the dynamics can reveal the nature of unconventional pseudospectrum of the non-normal Hamiltonian. In particular, we focus on the transient dynamics of the norm of an unnormalized quantum state evolved with the non-normal Hamiltonian, which is related to the probability for observing the trajectory with no quantum jump. We formulate the transient suppression of the decay rate of the norm due to the pseudospectral behavior and derive a non-Hermitian/non-normal analog of the time-energy uncertainty relation. We also consider two methods to experimentally realize the non-normal dynamics and observe our theoretical findings on quantum computers: one uses a technique to realize non-unitary operations on quantum circuits and the other leverages a quantum-classical hybrid algorithm called variational quantum simulation. Our demonstrations using cloud-based quantum computers provided by IBM Quantum exhibit the frozen dynamics of the norm in transient time, which can be regarded as a non-normal analog of the quantum Zeno effect.

cond-mat.mes-hall↗