arXiv subjects

Tsuneya Yoshida

Publications and source records attributed to Tsuneya Yoshida.

At least 19 recordsLinked to original sources

arXiv2026

Topological characterization of multifold band degeneracies in Altland-Zirnbauer symmetry classes

Topological degeneracies of energy bands in crystalline matter are conventionally characterized by invariants computed on an enclosing sphere over which the spectrum remains gapped, a program completed for minimal degeneracies in all ten Altland-Zirnbauer (AZ) symmetry classes. Higher-order degeneracies have instead been studied almost exclusively under crystalline-symmetry protection. Here, we characterize generic $n$-fold degeneracies stabilized solely by AZ symmetries acting locally in momentum space. Their codimension grows quadratically with $n$, placing multifold nodes in parameter spaces combining momenta with tuning parameters or synthetic dimensions. Crucially, the enclosing-sphere paradigm faces a fundamental obstruction: two $(n\,{-}\,1)$-fold degeneracy loci emanating from the $n$-fold node necessarily pierce every choice of enclosing sphere, leaving no uniform spectral gap and thus no standard homotopy classification. We elevate this obstruction into the diagnostic itself. Namely, on the two nodal manifolds where the loci cross the sphere, complementary spectral gaps are restored, admitting conventional band invariants (Chern numbers, Stiefel-Whitney classes, and winding numbers). This observation establishes a general two-way correspondence: (1) the multifold node is topologically protected whenever the associated nodal manifolds are robustly linked, and (2) invariants on cycles of one manifold encode their linking numbers with cycles of the other. Carrying out this program for minimal models of all ten AZ classes, we recast multifold band topology as the topology of linked nodal manifolds and lay the foundation for characterizing multifold nodes in models with arbitrarily many bands.

cond-mat.mes-hall↗

arXiv2026

Nonlinear Frequency-Momentum Topology and Doubling of Multifold Exceptional Points

Even in the linear limit, the topology of multifold (also called higher-order) exceptional points across the Brillouin zone has lacked a general characterization, leaving the doubling theorem essentially limited to two-fold exceptional points. Here, we establish the doubling theorem of $n$-fold exceptional points [EP$n$s ($n=2,3,\ldots$)] for systems where nonlinearity enters through eigenvalues. To this end, we introduce new topological invariants, termed frequency-momentum winding numbers, which characterize nonlinear EP$n$s in $m$-band systems throughout the Brillouin zone for arbitrary $n$ and $m$ ($m\geq n$). These invariants enable a unified proof of the doubling theorem in the absence of symmetry and under several symmetry constraints, including parity-time ($PT$) and charge-conjugation-parity symmetries. Furthermore, even in the linear limit, the frequency-momentum winding number indicates $\mathbb{Z}$ topology of $PT$-symmetric EP$2$s which is beyond the previously reported $\mathbb{Z}_2$ topology. The frequency-momentum winding numbers can also be extended to a class of coupled resonators in which nonlinearity enters via the eigenvectors, whereas the spectrum is determined by a nonlinear scalar equation for the frequency.

cond-mat.mes-hall↗

arXiv2026

Interaction-Enabled Two- and Three-Fold Exceptional Points

We propose a novel type of exceptional points, dubbed interaction-enabled $n$-fold exceptional points [EP$n$s ($n=2,3$)] -- EP$n$s protected by topology that are prohibited at the non-interacting level. Specifically, we demonstrate that both bosonic and fermionic systems host such interaction-enabled EP$n$s ($n=2,3$) in parameter space that are protected by charge U(1), pseudo-spin-parity, and $PT$ symmetries. The interaction-enabled EP2s are protected by zero-dimensional topology and give rise to qualitative changes in the loss rate, an experimentally measurable quantity for cold atoms. Furthermore, we reveal that interactions enable EP3s protected by one-dimensional topology beyond the point-gap topological classifications, suggesting the potential presence of a broader class of interaction-enabled non-Hermitian degeneracies.

cond-mat.mes-hall↗

arXiv2026

Liouvillian skin effects in two-dimensional electron systems at finite temperatures

Liouvillian skin effects, manifested as the localization of Liouvillian eigenstates around the boundary, are distinctive features of non-Hermitian systems and are particularly notable for their impact on system dynamics. Despite their significance, Liouvillian skin effects have not been sufficiently explored in electron systems. In this work, we demonstrate that a two-dimensional electron system on a substrate exhibits $\mathbb{Z}$ and $\mathbb{Z}_2$ Liouvillian skin effects due to the interplay among energy dissipations, spin-orbit coupling, and a transverse magnetic field. In addition, our analysis of the temperature dependence reveals that these Liouvillian skin effects become pronounced below the energy scale of band splitting induced by the spin-orbit coupling and the magnetic field. While our $\mathbb{Z}$ Liouvillian skin effect leads to charge accumulation under quench dynamics, its relaxation time is independent of the system size, in contrast to that of previously reported Liouvillian skin effects. This difference is attributed to the scale-free behavior of the localization length, which is analogous to non-Hermitian critical skin effects.

cond-mat.mes-hall↗

arXiv2026

Hopf Exceptional Points

Exceptional points at which eigenvalues and eigenvectors of non-Hermitian matrices coalesce are ubiquitous in the description of a wide range of platforms from photonic or mechanical metamaterials to open quantum systems. Here, we introduce a class of Hopf exceptional points (HEPs) that are protected by the Hopf invariants (including the higher-dimensional generalizations) and which exhibit phenomenology sharply distinct from conventional exceptional points. Saliently, owing to their $\mathbb{Z}_2$ topological invariant related to the Witten anomaly, three-fold HEPs and symmetry-protected five-fold HEPs act as their own ``antiparticles". Furthermore, based on higher homotopy groups of spheres, we predict the existence of multifold HEPs and symmetry-protected HEPs with non-Hermitian topology captured by a range of finite groups (such as $\mathbb{Z}_3$, $\mathbb{Z}_{12}$, or $\mathbb{Z}_{24}$) beyond the periodic table of Bernard-LeClair symmetry classes.

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

Topological photonics of generalized and nonlinear eigenvalue equations

Topological photonics is developed based on the analogy of Schrödinger equation which is mathematically reduced to a standard eigenvalue equation. Notably, several photonic systems are beyond the standard topological band theory as they are described by generalized or nonlinear eigenvalue equations. In this article, we review the topological band theory of this category. In the first part, we discuss topological photonics of generalized eigenvalue equations where the band structure may take complex values even when the involved matrices are Hermitian. These complex bands explain the characteristic dispersion relation of hyperbolic metamaterials. In addition, our numerical analysis predicts the emergence of symmetry-protected exceptional points in a photonic crystal composed of negative index media. In the second part, by introducing auxiliary bands, we establish the nonlinear bulk-edge correspondence under ``weak" nonlinearity of eigenvalues. The nonlinear bulk-edge correspondence elucidates the robustness of chiral edge modes in photonic systems where the permittivity and permeability are frequency dependent.

physics.optics↗

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

Winding Topology of Multifold Exceptional Points

Despite their ubiquity, a systematic classification of multifold exceptional points, $n$-fold spectral degeneracies (EP$n$s), remains a significant unsolved problem. In this article, we characterize the Abelian eigenvalue topology of generic EP$n$s and symmetry-protected EP$n$s for arbitrary $n$. The former and the latter emerge in a $(2n-2)$- and $(n-1)$-dimensional parameter space, respectively. By introducing topological invariants called resultant winding numbers, we elucidate that these EP$n$s are stable due to topology of a map from a base space (momentum or parameter space) to a sphere defined by resultants. In a $D$-dimensional parameter space ($D\geq c$), the resultant winding number topologically characterize a $(D-c)$-dimensional manifold of generic [symmetry-protected] EP$n$s whose codimension is $c=2n-2$ [$c=n-1$]. Our framework implies fundamental doubling theorems for both generic EP$n$s and symmetry-protected EP$n$s in $n$-band models.

cond-mat.mes-hall↗

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

Hinge non-Hermitian skin effect in the single-particle properties of a strongly correlated f-electron system

Non-Hermitian systems exhibit novel phenomena without Hermitian counterparts, such as exceptional points and the non-Hermitian skin effect. These non-Hermitian topological phenomena are observable in single-particle excitations of correlated systems in equilibrium, which are described by Green's functions. In this paper, we demonstrate the appearance of the hinge non-Hermitian skin effect in the effective Hamiltonian that describes the single-particle properties of an $f$-electron system. Skin effects result in a strong sensitivity to boundary conditions, and a large number of eigenstates localize at one boundary when open boundary conditions are applied. Our system exhibits such sensitivity and hosts skin modes localized around hinges. This hinge skin effect is induced by a non-Hermitian topology of the surface Brillouin zone. The hinge skin modes are observed for one-dimensional subsystems located between one pair of exceptional points in the surface Brillouin zone. This paper highlights that correlated materials are an exciting platform for analyzing non-Hermitian phenomena.

cond-mat.str-el↗

arXiv2024

Band structures of generalized eigenvalue equation and conic section

Band structures of several metamaterials are described by generalized eigenvalue equations where complex bands emerge even if the involved matrices are Hermitian. In this paper, we provide a geometrical understanding of the real-complex transition of the band structures. Specifically, our analysis, based on auxiliary eigenvalues, elucidates the correspondence between the real-complex transition of the generalized eigenvalue equations and Lifshitz transition in electron systems. Furthermore, we elucidate that real (complex) bands of a photonic system correspond to the Fermi surfaces of type-II (type-I) Dirac cones in electron systems when the permittivity $\varepsilon$ and the permeability $μ$ are independent of frequency. In addition, our analysis elucidates that EPs are induced by the frequency dependence of the permittivity $\varepsilon$ and the permeability $μ$ in our photonic system.

physics.optics↗

arXiv2024

Exceptional points and non-Hermitian skin effects under nonlinearity of eigenvalues

Band structures of metamaterials described by a nonlinear eigenvalue problem are beyond the existing topological band theory. In this paper, we analyze non-Hermitian topology under the nonlinearity of eigenvalues. Specifically, we elucidate that such nonlinear systems may exhibit exceptional points and non-Hermitian skin effects which are unique non-Hermitian topological phenomena. The robustness of these non-Hermitian phenomena is clarified by introducing the topological invariants under nonlinearity which reproduce the existing ones in linear systems. Furthermore, our analysis elucidates that exceptional points may emerge even for systems without an internal degree of freedom where the equation is single component. These nonlinearity-induced exceptional points are observed in mechanical metamaterials, e.g., the Kapitza pendulum.

cond-mat.mes-hall↗

arXiv2024

Non-Hermitian $\mathbb{Z}_4$ skin effect protected by glide symmetry

Although nonsymmorphic symmetry protects $\mathbb{Z}_4$ topology for Hermitian systems, non-Hermitian topological phenomena induced by such a unique topological structure remain elusive. In this paper, we elucidate that systems with glide symmetry exhibit non-Hermitian skin effects (NHSE) characterized by $\mathbb{Z}_4$ topology. Specifically, numerically analyzing a two-dimensional toy model, we demonstrate that the $\mathbb{Z}_4$ topology induces the NHSE when the topological invariant takes $ν=1,2$. Furthermore, our numerical analysis demonstrates that the NHSE is destroyed by perturbations preserving the relevant symmetry when the $\mathbb{Z}_4$-invariant takes $ν=4$.

cond-mat.mes-hall↗

arXiv2024

Non-Hermitian Mott Skin Effect

We propose a novel type of skin effects in non-Hermitian quantum many-body systems which we dub a non-Hermitian Mott skin effect. This phenomenon is induced by the interplay between strong correlations and the non-Hermitian point-gap topology. The Mott skin effect induces extreme sensitivity to the boundary conditions only in the spin degree of freedom (i.e., the charge distribution is not sensitive to boundary conditions), which is in sharp contrast to the ordinary non-Hermitian skin effect in non-interacting systems. Concretely, we elucidate that a bosonic non-Hermitian chain exhibits the Mott skin effect in the strongly correlated regime by closely examining an effective Hamiltonian. The emergence of the Mott skin effect is also supported by numerical diagonalization of the bosonic chain. The difference between the ordinary non-Hermitian skin effect and the Mott skin effect is also reflected in the time-evolution of physical quantities; under the time-evolution spin accumulation is observed while the charge distribution remains spatially uniform.

cond-mat.str-el↗

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↗

arXiv2023

Bulk-edge correspondence for nonlinear eigenvalue problems

Although topological phenomena attract growing interest not only in linear systems but also in nonlinear systems, the bulk-edge correspondence under the nonlinearity of eigenvalues has not been established so far. We address this issue by introducing auxiliary eigenvalues. We reveal that the topological edge states of auxiliary eigenstates are topologically inherited as physical edge states when the nonlinearity is weak but finite (i.e., auxiliary eigenvalues are monotonic as for the physical one). This result leads to the bulk-edge correspondence with the nonlinearity of eigenvalues.

cond-mat.mes-hall↗

arXiv2023

$\mathbb{Z}_2$ Non-Hermitian skin effect in equilibrium heavy-fermions

We demonstrate that a correlated equilibrium $f$-electron system with time-reversal symmetry can exhibit a $\mathbb{Z}_2$ non-Hermitian skin effect of quasi-particles. In particular, we analyze a two-dimensional periodic Anderson model with spin-orbit coupling by combining the dynamical mean-field theory (DMFT) and the numerical renormalization group. We prove the existence of the $\mathbb{Z}_2$ skin effect by explicitly calculating the topological invariant and show that spin-orbit interaction is essential to this effect. Our DMFT analysis demonstrates that the $\mathbb{Z}_2$ skin effect of quasi-particles is reflected on the pseudo-spectrum. Furthermore, we analyze temperature effects on this skin effect using the generalized Brillouin zone technique, which clarifies that the skin modes are strongly localized above the Kondo temperature.

cond-mat.str-el↗