arXiv subjects

Yasuhiro Hatsugai

Publications and source records attributed to Yasuhiro Hatsugai.

At least 19 recordsLinked to original sources

arXiv2025

Quasi-periodic flat-band model constructed by molecular-orbital representation

We construct a tight-binding model that hosts both a quasi-periodic nature and marcoscopically-dengenerate zero-energy modes. The model can be regarded as a counterpart of the Aubry-André-Harper (AAH) model, which is a paradigmatic example of the quasi-periodic tight-binding model. Our main focus is on the many-body state where the flat-band-like degenerate zero-energy modes are fully occupied. We find a characteristic sublattice dependence of the particle density distribution. Further, by analyzing the hyperuniformity of the particle density distribution, we find that it belongs to the class-I hyperuniform distribution, regardless of the model parameter. We also show that, upon changing the parameter, the finite-energy modes exhibit the same extended-to-localized transition as that for the original AAH model.

cond-mat.mes-hall↗

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

Topological pump and its plateau transitions of $N$-leg spin ladder

A topological pump on an $N\textrm{-}$leg spin ladder is discussed by introducing spatial clusterization whose adiabatic limit is a set of $2N\textrm{-}$site staircase clusters. We set a pump path in the parameter space that connects two different symmetry protected topological phases. By introducing a symmetry breaking staggered magnetic field, the system is always gapped during the pump. In the topological pump {thus obtained}, the bulk Chern number is given by the number of the critical points enclosed by the pump path. Plateau transitions characterized by the Chern number are demonstrated associated with deformation of the pump path. We find that there are $N$ critical points enclosed by the pump path for the $N\textrm{-}$leg ladder. The ground state phase diagram without symmetry breaking terms is numerically investigated by using the quantized Berry phase. We also discuss the physical picture of edge states in the diagonal boundary, and numerically demonstrate the bulk-edge correspondence for $N=2,3$ cases.

cond-mat.stat-mech↗

arXiv2025

Topological-to-Topological Transition Induced by On-Site Nonlinearity in a One-Dimensional Topological Insulator

Recent studies have extended the notion of band topology to nonlinear systems by defining nonlinear counterparts of eigenvalue problems. They have found the nonlinearity-induced topological transition, while it has required complicated nonlinearity such as off-diagonal one. Thus, the existence of nonlinearity-induced transitions has been unclear under homogeneous on-site nonlinearity, which is ubiquitously found in nature. We here reveal that such on-site nonlinearity can induce transitions of topological modes, where topological modes converging to zero begin to converge to nonzero values. Since such nonlinearity-induced transition remains the bulk band topology unchanged, we can regard it as a transition from a conventional topological mode to one unique to nonlinear systems. We analyze a nonlinear eigenvalue problem by rewriting it to a dynamical system in the spatial direction and clarify that the nonlinearity-induced transition is a result of the bifurcation in the spatial dynamics. We also propose a possible setup to observe the nonlinearity-induced transition that uses a gradual amplification of nonlinear waves. These results provide a general designing principle of topological insulators controlled by nonlinearity.

cond-mat.mes-hall↗

arXiv2024

Evolution of flat bands in two-dimensional fused pentagon network

Theoretical quest of flat-band tight-binding models usually relies on lattice structures on which electrons reside. Typical examples of candidate lattice structures include the Lieb-type lattices and the line graphs. Meanwhile, there can be accidental flat-band systems that belong to neither of such typical classes and deriving flat-band energies and wave functions for such systems is not straightforward. In this work, we investigate the characteristic band structure for the tight-binding model on a network composed of pentagonal rings, which is inspired by the theoretically-predicted carbon-based material. Although the lattice does not belong to conventional classes of flat band models, the exact flat bands appear only for fine-tuned parameters. We analytically derive the exact eigenenergies and eigenstates of the flat bands. By using the analytic form of the Bloch wave function, we construct the corresponding Wannier function and reveal its characteristic real-space profile. We also find that, even away from the exact flat-band limits, the nearly flat band exists near the Fermi level for the half-filled systems, which indicates that the present system will be a suitable platform for questing flat-band-induced correlated electron physics if it is realized in the real material.

cond-mat.mtrl-sci↗

arXiv2024

Topological domain-wall pump with $\mathbb{Z}_2$ spontaneous symmetry breaking

A domain-wall pump by an extended cluster model of $S=1/2$ spins is proposed with local $U(1)$ gauge invariance. Its snapshot ground state is gapped and doubly degenerated due to $\mathbb{Z}_2$ invariance, which is broken by an infinitesimal boundary magnetic field. The ground state associated with the spontaneous symmetry breaking (SSB) is still symmetry-protected with additional spatial inversion that is characterized by the $\mathbb{Z}_2$ Berry phase. We investigate the topological domain-wall pump with/without boundaries. The topological pump associated with the inversion symmetry-breaking path induces a non-trivial Chern number of bulk and a singular behavior of edge states of the domain-wall. Generalization to the multi-spin interaction is also explicitly given.

cond-mat.str-el↗

arXiv2024

Hidden chiral symmetry for kagome lattice and its analogs

Chiral symmetry plays an essential role in condensed matter physics. In tight-binding models, it is often attributed to bipartite lattice structures, and its typical consequence is the ``particle-hole symmetric" band structures, that is, the positive and negative eigenenergies appear in a pairwise manner. In this work, we address the chiral symmetry for non-bipartite lattice models with flat bands. Our argument relies on what we call the molecular-orbital representation, by which we can guarantee the existence of the flat band. We show that the chiral symmetry is preserved for the non-flat bands when the molecular orbitals are normalized and divided into two sets within which they are non-overlapping. The chiral operator is constructed by the same molecular orbitals as the Hamiltonian. This results in the characteristic relation between the chiral operator and the Hamiltonian, which we call the Pythagoras relation. We present the examples of such models, i.e., the kagome lattice and its one-dimensional analog, and address the characteristics originating from the chiral symmetry, such as the emergence of the topological edge modes. We also show an example where the numbers of molecular orbitals in each set are different from each other, resulting in multiple flat bands with different energies.

cond-mat.mes-hall↗

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↗

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

Blocking particle dynamics in diamond chain with spatially increasing flux

Spatial non-uniformity in tight-binding models serves as a source of rich phenomena. In this paper, we study a diamond-chain tight-binding model with a spatially-modulated magnetic flux at each plaquette. In the numerical studies with various combinations of the minimum and maximum flux values, we find the characteristic dynamics of a particle, namely, a particle slows down when approaching the plaquette with $π$-flux. This originates from the fact that the sharply localized eigenstates exist around the $π$-flux plaquette. These localized modes can be understood from a squared model of the original one. This characteristic blocked dynamics will be observed in photonic waveguides or cold atoms.

cond-mat.mes-hall↗

arXiv2023

A symmetry-protected exceptional ring in a photonic crystal with negative index media

Non-Hermitian topological band structures such as symmetry-protected exceptional rings (SPERs) can emerge for systems described by the generalized eigenvalue problem (GEVP) with Hermitian matrices. In this paper, we numerically analyze a photonic crystal with negative index media, which is described by the GEVP with Hermitian matrices. Our analysis using COMSOL Multiphysics demonstrates that a SPER emerges for photonic crystals composed of split-ring resonators and metal-wire structures. We expect that the above SPER can be observed in experiments as it emerges at a finite frequency.

cond-mat.mes-hall↗

arXiv2023

$Z_2\times Z_2$ symmetry and $Z_4$ Berry phase of bosonic ladder

Bose gas on a two-leg ladder exhibits an interesting topological phase. We show the presence of a bosonic symmetry-protected-topological (SPT) phase protected by $Z_2\times Z_2$ symmetry. This symmetry leads to $Z_4$ fractional quantization of $Z_4$ Berry phase, that is a topological order parameter to identify the bulk. Using the $Z_4$ Berry phase, we have shown that the interacting bosonic system possesses rich topological phases depending on particle density and strength of interaction. Based on the bulk-edge correspondence, each edge state of the SPT phases is discussed in relation to the $Z_4$ Berry phases. Especially we have found an intermediate phase that is not adiabatically connected to a simple adiabatic limit, that possesses unconventional edge states, which we have numerically demonstrate by employing the density-matrix-renormalization group algorithm.

cond-mat.quant-gas↗

arXiv2023

Unconventional gapless semiconductor in an extended martini lattice in covalent honeycomb materials

We study characteristic electronic structures in an extended martini lattice model and propose its materialization in $π$-electron networks constructed by designated chemisorption on graphene and silicene. By investigating the minimal tight-binding model, we reveal rich electronic structures tuned by the ratio of hopping parameters, ranging from the band insulator to the unconventional gapless semiconductor. Remarkably, the unconventional gapless semiconductor is characterized by a flat band at the Fermi level. Further, the density functional theory calculations for candidate materials reveal that the characteristic electronic structures can be realized by designated chemisorption or chemical substitution on graphene and silicene, and that the electronic structure near the Fermi level is tunable by the choice of the atomic species of adsorbed atoms. Our results open the way to search exotic electronic structures and their functionalities induced by an extended martini lattice.

cond-mat.mtrl-sci↗

arXiv2023

Molecular-orbital representation with random U(1) variables

We propose random tight-binding models that host macroscopically degenerate zero energy modes and belong to the unitary class. Specifically, we employ the molecular-orbital representation, where a Hamiltonian is constructed by a set of non-orthogonal orbitals composed of linear combinations of atomic orbitals. By setting the coefficients appearing in molecular orbitals to be random U(1) variables, we can make the models belong to the unitary class. We find two characteristic behaviors that are distinct from the random-real-valued molecular-orbital model. Firstly, a finite energy gap opens on top of the degenerate zero energy modes. Secondly, besides the zero energy modes, we also argue that the band center of the finite energy modes is critical, which is inherited from the dual counterpart, namely, the random-phase model on a bipartite lattice. Furthermore, as a by-product of this model-construction scheme, we also construct the random tight-binding model on a composite lattice, where we also find a realization of critical states.

cond-mat.mes-hall↗

arXiv2023

Higher-Order Topological Insulator on a Martini Lattice and Its Square Root Descendant

Notion of square-root topological insulators have been recently generalized to higher-order topological insulators. In two-dimensional square-root higher-order topological insulators, emergence of in-gap corner states are inherited from the squared Hamiltonian which hosts higher-order topology. In this paper, we propose that the martini lattice model serves as a concrete example of higher-order topological insulators. Furthermore, we also propose a suquare-root higher-order topological insulator based on the martini model. Specifically, we propose that the honeycomb lattice model with two-site decoration, whose squared Hamiltonian consists of two martini lattice models, realizes square-root higher-order topological insulators. We show, for both of these two models, that in-gap corner states appear at finite energies and that they are portected by non-trivial bulk $\mathbb{Z}_3$ topological invariant.

cond-mat.mes-hall↗

arXiv2023

Fate of exceptional points under interactions: Reduction of topological classifications

Despite recent extensive studies of the non-Hermitian topology, understanding interaction effects is left as a crucial question. In this paper, we address interaction effects on exceptional points which are protected by the non-trivial point-gap topology unique to non-Hermitian systems. Our analysis in a two-dimensional parameter space elucidates the existence of exceptional points and symmetry-protected exceptional rings fragile against interactions; they are topologically protected only in non-interacting cases. This fragility of exceptional points and symmetry-protected exceptional rings arises from the reduction of non-Hermitian topological classifications, which is elucidated by introducing topological invariants of the second-quantized Hamiltonian for both non-interacting and interacting cases. These topological invariants are also available to analyze the reduction phenomena of gapped systems. The above results strongly suggest similar reduction phenomena of exceptional points in generic cases and open up a new direction of research in the non-Hermitian topology.

cond-mat.mes-hall↗

arXiv2022

Topological pump of $SU(Q)$ quantum chain and Diophantine equation

A topological pump of the $SU(Q)$ quantum chain is proposed associated with a current due to a local $[U(1)]^{\otimes Q}$ gauge invariance of colored fermions. The $SU(Q)$ invariant dimer phases are characterized by the $Z_Q$ Berry phases as a topological order parameter with a $d$-dimensional twist space ($d=Q-1$) as a synthetic Brillouin zone. By inclusion of the symmetry breaking perturbation specified by a rational parameter $Φ=P/Q$, the pump, that encloses around the phase boundary, is characterized by the $Q$ Chern numbers associated with the currents due to uniform infinitesimal twists. The analysis of the systems under the open/periodic/twisted boundary conditions clarifies the bulk-edge correspondence of the pump where the large gauge transformation generated by the center of mass (CoM) plays a central role. An explicit formula for the Chern number is given by using the Diophanine equation. Numerical demonstration by the exact diagonalization and the DMRG for finite systems ($Q=3,4$ and $5$) have been presented to confirm the general discussions for low energy spectra, edge states, CoM's, Chern numbers and the bulk-edge correspondence. A modified Lieb-Schultz-Mattis type argument for the general $SU(Q)$ quantum chain is also mentioned.

cond-mat.str-el↗