arXiv subjects

Kohei Kawabata

Publications and source records attributed to Kohei Kawabata.

At least 19 recordsLinked to original sources

arXiv2026

Quantum geometry of the non-Hermitian skin effect

The non-Hermitian skin effect is nonreciprocity-induced localization phenomena in which a macroscopic number of eigenstates accumulate anomalously at the boundary, accompanied by the extreme sensitivity to boundary conditions. Here, we develop a geometric characterization of the non-Hermitian skin effect. We demonstrate that the localization length scale associated with the skin effect is encoded in the quantum metric defined solely from right eigenstates, but not in the biorthogonal quantum metric. Moreover, we show that the quantum metrics can exhibit the power-law divergences at gapless points that depend on the different boundary conditions. We also reveal that cusps of the generalized Brillouin zone in non-Bloch band theory are signaled by discontinuities in the quantum metrics. We illustrate these behavior using prototypical non-Hermitian models, such as the Hatano-Nelson model and the non-Hermitian, nonreciprocal Su-Schrieffer-Heeger model.

cond-mat.mes-hall↗

arXiv2026

Extracting Boundary Conformal Data from Periodic Non-Hermitian Critical Chains

Boundary conformal field theory (BCFT) contains universal data that are usually accessed microscopically by imposing spatial boundaries on the lattice. In non-Hermitian many-body systems, however, changing boundary conditions can qualitatively reorganize spectra and eigenstates, and their boundary criticality remains elusive. Here, we introduce a periodic-chain spectroscopy to extract universal boundary quantities, such as the Affleck-Ludwig $g$-factor, directly from non-Hermitian bulk-critical quantum chains, avoiding the need to engineer microscopic open boundaries and circumventing subtle boundary effects in non-Hermitian systems. We illustrate our method with a $\mathcal{PT}$-symmetric Ising realization of the real nonunitary Yang-Lee CFT and reveal a universal negative excited-to-ground ratio, which has no counterpart in unitary critical theories and provides a microscopic signature of nonunitarity. For the genuinely complex fixed points of the non-Hermitian five-state Potts chain, we extract intrinsically complex boundary coefficients, verify the exact Kramers-Wannier duality relation, and select the consistent analytic-continuation branch of the boundary states. Our results establish a route to nonunitary BCFT universal data using only knowledge of the bulk critical system, opening a window into non-Hermitian boundary criticality.

cond-mat.stat-mech↗

arXiv2026

Complex nonlinear sigma model

Motivated by the recent interest in the criticality of open quantum many-body systems, we study nonlinear sigma models with complexified couplings as a general framework for nonunitary field theory. Applying the perturbative renormalization-group analysis to the tenfold symmetric spaces, we demonstrate that fixed points with complex scaling dimensions and critical exponents arise generically, without counterparts in conventional nonlinear sigma models with real couplings. We further clarify the global phase diagrams in the complex-coupling plane and identify both continuous and discontinuous phase transitions. Our work thus identifies nonlinear sigma models as a representative setting for studying complex critical points and elucidates universal aspects of critical phenomena in complexified field theory.

cond-mat.stat-mech↗

arXiv2026

Symmetry and Topology of Monitored Quantum Dynamics

The interplay between unitary dynamics and quantum measurements induces diverse phenomena in open quantum systems with no counterparts in closed quantum systems at equilibrium. Here, we generally classify Kraus operators and their effective non-Hermitian dynamical generators, thereby establishing the tenfold classification for symmetry and topology of monitored free fermions. Our classification elucidates the role of topology in measurement-induced phase transitions and identifies potential topological terms in the corresponding nonlinear sigma models. Furthermore, we establish the bulk-boundary correspondence in monitored quantum dynamics: nontrivial topology in spacetime manifests itself as topologically nontrivial steady states and gapless boundary states in Lyapunov spectra, such as Lyapunov zero modes and chiral edge modes, leading to the topologically protected slowdown of dynamical purification.

cond-mat.stat-mech↗

arXiv2026

Quantum transport on Bethe lattices with non-Hermitian sources and a drain

We consider quantum transport in a tight-binding model on the Bethe lattice of finite generation, which we expect to be the first step toward analyzing electronic transport in a light-harvesting molecule. We seek conditions under which the electronic current from the peripheral light-harvesting sites to the central site reaches its maximum. As a new feature for analyzing quantum transport, we add complex potentials for sources at peripheral sites and a drain at the central site, and solve a non-Hermitian eigenvalue problem, instead of simulating an initial-value problem. Solving the eigenvalue problem clearly reveals which electronic channels contribute most to the quantum transport. The number of eigenstates that can penetrate from the peripheral sites to the central site is quite limited among the total number of eigenstates. All the other eigenstates are localized around the peripheral sites and cannot reach the central site. The former eigenstates can carry current, reducing the problem to quantum transport on a parity-time ($\PT$)-symmetric tight-binding chain. The current has a maximum with respect to the strengths of the sources and the drain. The current decreases as we increase the strengths beyond the maximum and vanishes in the limit of infinite strength. Moreover, the current maximum is given by a zero mode. When the number of links is common to all generations, the current takes the maximum value at the exceptional point where two eigenstates coalesce to a zero mode, which emerges because of the non-Hermiticity due to the $\PT$-symmetric complex potentials. By introducing randomness either into the hopping amplitude or the number of links in each generation of the tree, we obtain a random-hopping tight-binding model, in which the current reaches its maximum not exactly, but approximately, for a zero mode, although it is no longer located at an exceptional point in general.

quant-ph↗

arXiv2026

Continuum Landau surface states in a non-Hermitian Weyl semimetal

The surface states of certain topological phases can be linked to a quantum anomaly: the violation of a classical symmetry by a field theory via a non-conserved current. This has been generalized to the case of a non-Hermitian (NH) chiral anomaly affecting the surfaces states of an NH Weyl phase. Here, we show that the NH anomaly inflow is mediated by continnum Landau modes (CLMs): special eigenstates exhibiting both spatial localization and a continuous spectrum, contrary to the usual distinction between bound and free states. The number of anomaly-induced surface modes scales with the sample volume rather than its surface area, which is shown to be tied to the unusual multiplicity of the CLMs. The other properties of the CLMs, including their normalization conditions and localization scale, closely match the predictions of the NH field theory. Finally, we discuss the conditions under which these phenomena can be probed experimentally using metamaterials.

cond-mat.mes-hall↗

arXiv2026

Quantum walk with a local spin interaction

We introduce a model of quantum walkers interacting with a magnetic impurity localized at the origin. First, we study a model of a single quantum walker interacting with a localized magnetic impurity. For a simple case of parameter values, we analytically obtain the eigenvalues and the eigenvectors of bound states, in which the quantum walker is bound to the magnetic impurity. Second, we study a model with two quantum walkers and one magnetic impurity, in which the two quantum walkers indirectly interact with each other via the magnetic impurity, as in the Kondo model. We numerically simulate the collision dynamics when the spin-spin interaction at the origin is of the XX type and the SU(2) Heisenberg type. In the case of the XX interaction, we calculate the entanglement negativity to quantify how much the two quantum walkers are entangled with each other, and find that the negativity increases drastically upon the collision of the two walkers. We compare the time dependence for different statistics, namely, fermionic, bosonic, and distinguishable walkers. In the case of the SU(2) interaction, we simulate the dynamics starting from the initial state in which one fermionic walker is in a bound eigenstate around the origin and the other fermionic walker is a delta function colliding with the first walker. We find that a bound eigenstate closest to the singlet state of the first walker and the magnetic impurity is least perturbed by the collision of the second walker. We speculate that this is a manifestation of Kondo physics at the lowest level of the real-space renormalization-group procedure.

quant-ph↗

arXiv2026

Non-Hermitian Disordered Systems

Non-Hermitian disordered systems have emerged as a central arena in modern physics, with ramifications spanning condensed matter, quantum, statistical, and high energy contexts. The same principles also underlie phenomena beyond physics, such as network science, complex systems, and biophysics, where dissipation, nonreciprocity, and stochasticity are ubiquitous. Here, we review the physics and mathematics of non-Hermitian disordered systems, with particular emphasis on non-Hermitian random matrix theory. We begin by presenting the 38-fold symmetry classification of non-Hermitian systems, contrasting it with the 10-fold way for Hermitian systems. After introducing the classic Ginibre ensembles of non-Hermitian random matrices, we survey various diagnostics for complex-spectral statistics and distinct universality classes realized by symmetry. As a key application to physics, we discuss how non-Hermitian random matrix theory characterizes chaos and integrability in open quantum systems. We then turn to the criticality due to the interplay of disorder and non-Hermiticity, including Anderson transitions in the Hatano-Nelson model and its higher-dimensional extensions. We also discuss the effective field theory description of non-Hermitian disordered systems in terms of nonlinear sigma models.

cond-mat.mes-hall↗

arXiv2025

Exceptional second-order topological insulators

Point-gap topological phases of non-Hermitian systems exhibit exotic boundary states that have no counterparts in Hermitian systems. Here, we develop classification of second-order point-gap topological phases protected by reflection symmetry. Based on this classification, we propose exceptional second-order topological insulators, exhibiting second-order boundary states stabilized by point-gap topology. As an illustrative example, we uncover a two-dimensional exceptional second-order topological insulator with point-gapless corner states. Furthermore, we identify a three-dimensional exceptional second-order topological insulator that features hinge states with isolated exceptional points, representing second-order topological phases intrinsic to non-Hermitian systems. Our work enlarges the family of point-gap topological phases in non-Hermitian systems.

cond-mat.mes-hall↗

arXiv2025

Non-linear sigma models for non-Hermitian random matrices in symmetry classes AI$^{\dagger}$ and AII$^{\dagger}$

Symmetry of non-Hermitian matrices underpins many physical phenomena. In particular, chaotic open quantum systems exhibit universal bulk spectral correlations classified on the basis of time-reversal symmetry$^{\dagger}$ (TRS$^{\dagger}$), coinciding with those of non-Hermitian random matrices in the same symmetry class. Here, we analytically study the spectral correlations of non-Hermitian random matrices in the presence of TRS$^{\dagger}$ with signs $+1$ and $-1$, corresponding to symmetry classes AI$^{\dagger}$ and AII$^{\dagger}$, respectively. Using the fermionic replica non-linear sigma model approach, we derive $n$-fold integral expressions for the $n$th moment of the one-point and two-point characteristic polynomials. Performing the replica limit $n\to 0$, we qualitatively reproduce the density of states and level-level correlations of non-Hermitian random matrices with TRS$^{\dagger}$.

quant-ph↗

arXiv2025

Hopf Bifurcation of Nonlinear Non-Hermitian Skin Effect

The non-Hermitian skin effect, nonreciprocity-induced anomalous localization of an extensive number of eigenstates, represents a hallmark of non-Hermitian topological systems with no analogs in Hermitian systems. Despite its significance across various open classical and quantum systems, the influence of nonlinearity has remained largely unclear. Here, we reveal the Hopf bifurcation of the nonlinear skin effect as a critical phenomenon unique to nonlinear non-Hermitian systems. We demonstrate that nonlinearity destabilizes skin states and instead gives rise to the emergence of delocalized states associated with limit cycles in phase space. We also uncover the algebraically localized critical skin effect precisely at the Hopf bifurcation point. We illustrate these behavior in a nonlinear extension of the Hatano-Nelson model in both continuum and lattice. Our work shows a significant role of nonlinearity in the skin effect and uncovers rich phenomena arising from the interplay between non-Hermiticity and nonlinearity.

cond-mat.mes-hall↗

arXiv2025

$K$-theory classification of Wannier localizability and detachable topological boundary states

A hallmark of certain topology, including the Chern number, is the obstruction to constructing exponentially localized Wannier functions in the bulk bands. Conversely, other types of topology do not necessarily impose Wannier obstructions. Remarkably, such Wannier-localizable topological insulators can host boundary states that are detachable from the bulk bands. In our accompanying Letter [D. Nakamura {\it et al.}, Phys. Rev. Lett. 135, 096601 (2025), arXiv:2407.09458], we demonstrate that non-Hermitian topology underlies detachable boundary states in Hermitian topological insulators and superconductors, thereby establishing their tenfold classification based on internal symmetry. Here, using $K$-theory, we elucidate the relationship between Wannier localizability and detachability of topological boundary states. From the boundary perspective, we classify intrinsic and extrinsic non-Hermitian topology, corresponding to nondetachable and detachable topological boundary states, respectively. From the bulk perspective, on the other hand, we classify Wannier localizability through the homomorphisms of topological phases from the tenfold Altland-Zirnbauer symmetry classes to the threefold Wigner-Dyson symmetry classes. Notably, these two approaches from the boundary and bulk perspectives lead to the same classification. We clarify this agreement and develop a unified understanding of the bulk-boundary correspondence on the basis of $K$-theory.

cond-mat.mes-hall↗

arXiv2025

Non-Hermitian Origin of Detachable Boundary States in Topological Insulators

While topology can impose obstructions to exponentially localized Wannier functions, certain topological insulators are exempt from such Wannier obstructions. The absence of the Wannier obstructions can further accompany topological boundary states that are detachable from the bulk bands. Here, we elucidate a close connection between these detachable topological boundary states and non-Hermitian topology. Identifying topological boundary states as non-Hermitian topology, we demonstrate that intrinsic non-Hermitian topology leads to the inevitable spectral flow. By contrast, we show that extrinsic non-Hermitian topology underlies the detachment of topological boundary states and clarify anti-Hermitian topology of the detached boundary states. Based on this connection and $K$-theory, we complete the tenfold classification of Wannier localizability and detachable topological boundary states.

cond-mat.mes-hall↗

arXiv2025

Non-Hermitian Hopf insulators

Hopf insulators represent a unique class of topological insulators that exist exclusively in two-band systems and are inherently unstable upon the inclusion of additional bands. Meanwhile, recent studies have shown that non-Hermiticity gives rise to distinctive complex-energy gap structures, known as point gaps, and associated topological phases with no analogs in Hermitian systems. However, non-Hermitian counterparts of Hopf insulators have remained largely elusive. Here, we generally classify topological phases of two-band non-Hermitian systems based on the homotopy theory and uncover Hopf-type point-gap topology present only for two bands. Specifically, we reveal such Hopf-type point-gap topology for three-dimensional systems with chiral symmetry (class AIII) and four-dimensional systems with no symmetry (class A). Explicitly constructing prototypical models from the Hermitian Hopf insulator, we further demonstrate that these non-Hermitian topological phases lead to anomalous point-gapless boundary states spectrally detachable from the bulk bands.

cond-mat.mes-hall↗

arXiv2025

Complex entanglement entropy for complex conformal field theory

Conformal field theory underlies critical ground states of quantum many-body systems. While conventional conformal field theory is associated with positive central charges, nonunitary conformal field theory with complex-valued central charges has recently been recognized as physically relevant. Here, we demonstrate that complex-valued entanglement entropy characterizes complex conformal field theory and critical phenomena of open quantum many-body systems. This is based on non-Hermitian reduced density matrices constructed from the combination of right and left ground states. Applying the density matrix renormalization group to non-Hermitian systems, we numerically calculate the complex entanglement entropy of the non-Hermitian five-state Potts model, thereby confirming the scaling behavior predicted by complex conformal field theory.

cond-mat.stat-mech↗

arXiv2025

Nonsymmorphic Topological Phases of Non-Hermitian Systems

Non-Hermiticity appears ubiquitously in various open classical and quantum systems and enriches classification of topological phases. However, the role of nonsymmorphic symmetry, crystalline symmetry accompanying fractional lattice translations, has remained largely unexplored. Here, we systematically classify non-Hermitian topological crystalline phases protected by nonsymmorphic symmetry and reveal unique phases that have no counterparts in either Hermitian topological crystalline phases or non-Hermitian topological phases protected solely by internal symmetry. Specifically, we elucidate the $\mathbb{Z}_2$ and $\mathbb{Z}_4$ non-Hermitian topological phases and their associated anomalous boundary states characterized by distinctive complex-valued energy dispersions.

cond-mat.mes-hall↗

arXiv2025

Universal Stochastic Equations of Monitored Quantum Dynamics

We investigate the monitored quantum dynamics of Gaussian mixed states and derive the universal Fokker-Planck equations that govern the stochastic time evolution of entire density-matrix spectra, obtaining their exact solutions. From these equations, we reveal an even-odd effect in purification dynamics: whereas entropy exhibits exponential decay for an even number $N$ of complex fermions, algebraic decay with divergent purification time occurs for odd $N$ as a manifestation of dynamical criticality. Additionally, we identify the universal fluctuations of entropy in the chaotic regime, serving as a non-unitary counterpart of the universal conductance fluctuations in mesoscopic electronic transport phenomena. Furthermore, we elucidate and classify the universality classes of non-unitary quantum dynamics based on fundamental symmetry. We also validate the universality of these analytical results through extensive numerical simulations across different types of models.

cond-mat.stat-mech↗

arXiv2025

Field theory of non-Hermitian disordered systems

The interplay between non-Hermiticity and disorder gives rise to unique universality classes of Anderson transitions. Here, we develop a field-theoretical description of non-Hermitian disordered systems based on fermionic replica nonlinear sigma models. We classify the target manifolds of the nonlinear sigma models across all the 38-fold symmetry classes of non-Hermitian systems and corroborate the correspondence of the universality classes of Anderson transitions between non-Hermitian systems and Hermitized systems with additional chiral symmetry. We apply the nonlinear sigma model framework to study the spectral properties of non-Hermitian random matrices with particle-hole symmetry. Furthermore, we demonstrate that the Anderson transition unique to nonreciprocal disordered systems in one dimension, including the Hatano-Nelson model, originates from the competition between the kinetic and topological terms in a one-dimensional nonlinear sigma model. We also discuss the critical phenomena of non-Hermitian disordered systems with symmetry and topology in higher dimensions.

cond-mat.dis-nn↗