arXiv subjects

Shu Hamanaka

Publications and source records attributed to Shu Hamanaka.

8 recordsLinked to original sources

arXiv2026

Multifractal Analysis of the Non-Hermitian Skin Effect: From Many-Body to Tree Models

The non-Hermitian skin effect is an anomalous localization phenomenon induced by nonreciprocal dissipation and has attracted considerable attention in recent years both theoretically and experimentally. In this article, we review the multifractal aspects of the non-Hermitian skin effect. In particular, we discuss how the many-body skin effect exhibits multifractality in many-body Hilbert space, unlike the trivial Hilbert-space occupation of the single-particle skin effect on crystalline lattices. We further highlight that the many-body skin effect can coexist with random-matrix spectral statistics, in contrast to the multifractality associated with many-body localization, which typically accompanies the absence of ergodicity. We also introduce a solvable model on a Cayley tree as an effective description of the many-body Hilbert space, in which the multifractal dimensions can be obtained analytically. This review provides a unified perspective on multifractal structures in the non-Hermitian skin effect across single-particle, many-body, and tree models, and clarifies their distinctive relation to ergodicity in open quantum systems.

cond-mat.dis-nn↗

arXiv2026

Koopman Nonlinear Non-Hermitian Skin Effect

Non-Hermitian skin effects are conventionally manifested as boundary localization of eigenstates in linear systems. In nonlinear settings, however, where eigenstates are no longer well defined, it becomes unclear how skin effects should be faithfully characterized. Here, we propose a Koopman-based characterization of nonlinear skin effects, in which localization is defined in terms of Koopman eigenfunctions in a lifted observable space, rather than physical states. Using a minimal nonlinear extension of the Hatano-Nelson model, we show that dominant Koopman eigenfunctions localize sharply on higher-order observables, in stark contrast to linear skin effects confined to linear observables. This lifted-space localization governs the sensitivity to boundary amplitude perturbations, providing a distinct dynamical signature of the nonlinear skin effect. Our results establish the Koopman framework as a natural setting in which skin effects unique to nonlinear non-Hermitian systems can be identified.

cond-mat.mes-hall↗

arXiv2025

Interacting Electronic Topology of Nonlocal Crystals

Nonlocal crystals are systems with translational symmetry but arbitrary range couplings or interactions between degrees of freedom. We argue that the notion of topology in such systems does not collapse to that in zero dimensions, as one may naively expect in view of the infinite interaction range. At the same time, we show that the range of available topological phases can be enriched in comparison to the case with local interactions. This is demonstrated by constructing an example of a fermionic symmetry-protected phase in one dimension in symmetry class AII with inversion symmetry, using a Hatsugai-Kohmoto-type model. The new phase exists only in a nonlocal crystal with electron-electron interactions and can be identified from symmetry eigenvalues. We construct an associated topological charge pump as a physical manifestation of its topology.

cond-mat.str-el↗

arXiv2025

Multifractal statistics of non-Hermitian skin effect on the Cayley tree

Multifractal analysis is a powerful tool for characterizing the localization properties of wave functions. Despite its utility, this tool has been predominantly applied to disordered Hermitian systems. Multifractal statistics associated with the non-Hermitian skin effect remain largely unexplored. Here, we demonstrate that the tree geometry induces multifractal statistics for the single-particle skin states on the Cayley tree by deriving the analytical expression of multifractal dimensions. This sharply contrasts with the absence of multifractal properties for conventional single-particle skin effects in crystalline lattices. Our work uncovers the unique feature of the skin effect on the Cayley tree and provides a novel mechanism for inducing multifractality in open quantum systems without disorder.

cond-mat.mes-hall↗

arXiv2025

Callan-Rubakov effects in topological insulators

The Callan-Rubakov effect describes monopole-catalyzed proton decay. While this effect is fundamental for quantum field theories, its experimental observation has remained far from reality. Here, we reveal a similar, but experimentally reachable, defect-catalysis of the quantum anomaly in topological materials. In particular, surface Dirac fermions on topological insulators develop a distinct localized state at the position of dislocations or $π$-fluxes, which mediates spin-flip time-reversal breaking scattering or absorption of electrons. Despite the Hermiticity of topological insulators, a non-Hermitian topological number guarantees the robust existence of the localized state. Our finding implies that non-magnetic defects may behave like magnetic impurities on surfaces of topological insulators. Using the K-theory classification, we generalize this condensed-matter version of the Callan-Rubakov effect to other classes of topological materials.

cond-mat.mes-hall↗

arXiv2025

Multifractality of many-body non-Hermitian skin effect

The non-Hermitian skin effect, anomalous localization of an extensive number of eigenstates induced by nonreciprocal dissipation, plays a pivotal role in non-Hermitian topology and significantly influences the open quantum dynamics. However, its genuinely quantum characterization in many-body systems has yet to be developed. Here, we elucidate that the skin effect manifests itself as multifractality in the many-body Hilbert space. This multifractality does not accompany the single-particle skin effect and hence is intrinsic to the many-body skin effect. Furthermore, we demonstrate that the many-body skin effect coexists with spectral statistics of random matrices, in contrast to multifractality associated with the many-body localization, which necessitates the absence of ergodicity. We also illustrate multifractality caused by the Liouvillian skin effect in Markovian open quantum systems. Our work establishes a defining characterization of the non-Hermitian skin effect and uncovers a fundamental relationship between multifractality and ergodicity in open quantum many-body systems.

cond-mat.str-el↗

arXiv2025

Non-Hermitian Topology in Hermitian Topological Matter

Non-Hermiticity gives rise to distinctive topological phenomena absent in Hermitian systems. However, connection between such intrinsic non-Hermitian topology and Hermitian topology has remained largely elusive. Here, considering the bulk and boundary as an environment and system, respectively, we demonstrate that anomalous boundary states in Hermitian topological insulators exhibit non-Hermitian topology. We study the self-energy capturing the particle exchange between the bulk and boundary, and show that it detects Hermitian topology in the bulk and induces non-Hermitian topology at the boundary. As an illustrative example, we reveal non-Hermitian topology and concomitant skin effect inherently embedded within chiral edge states of Chern insulators. We also identify the emergence of hinge states within effective non-Hermitian Hamiltonians at surfaces of three-dimensional topological insulators. Furthermore, we comprehensively classify our correspondence across all the tenfold symmetry classes of topological insulators and superconductors. Our work uncovers hidden connection between Hermitian and non-Hermitian topology, and provides an approach to identifying non-Hermitian topology in quantum matter.

cond-mat.mes-hall↗

arXiv2024

Interaction-induced Liouvillian skin effect in a fermionic chain with a two-body loss

Despite recent intensive research on topological aspects of open quantum systems, effects of strong interactions have not been sufficiently explored. In this paper, we demonstrate that complex-valued interactions induce the Liouvillian skin effect by analyzing a one-dimensional correlated model with two-body loss. We show that, in the presence of complex-valued interactions, eigenmodes and eigenvalues of the Liouvillian strongly depend on boundary conditions. Specifically, we find that complex-valued interactions induce localization of eigenmodes of the Liouvillian around the right edge under open boundary conditions. To characterize the Liouvllian skin effect, we define the topological invariant by using the Liouvillian superoperator. Then, we numerically confirm that the topological invariant captures the Liouvillian skin effect. Furthermore, the presence of the localization of eigenmodes results in the unique dynamics observed only under open boundary conditions: particle accumulation at the right edge in transient dynamics. Our result paves the way to realize topological phenomena in open quantum systems induced by strong interactions.

cond-mat.str-el↗