arXiv subjects

Yasuhiro Hatsugai

Publications and source records attributed to Yasuhiro Hatsugai.

At least 55 records · Page 3Linked to original sources

arXiv2021

Plateau transitions of spin pump and bulk-edge correspondence

Sequential plateau transitions of quantum spin chains ($S$=1,3/2,2 and 3) are demonstrated by a spin pump using dimerization and staggered magnetic field as synthetic dimensions. The bulk is characterized by the Chern number associated with the boundary twist and the pump protocol as a time. It counts the number of critical points in the loop that is specified by the $Z_2$ Berry phases. With open boundary condition, discontinuity of the spin weighted center of mass due to emergent effective edge spins also characterizes the pump as the bulk edge correspondence. It requires extra level crossings in the pump as a super-selection rule that is consistent with the Valence Bond Solid (VBS) picture.

cond-mat.stat-mech↗

arXiv2021

Dynamics governed by symmetry-protected exceptional rings for mechanical systems

Non-Hermitian topological phenomena occur in mechanical systems described by the Newton equation. A mechanical graphene, which is composed of mass points and springs, shows symmetry-protected exceptional rings (SPERs) in the presence of the friction. However, it remains unclear what physical properties or phenomena the SPERs induce. Our numerical analysis reveals that the SPERs can govern dynamics in the wavenumber space. Moreover, we propose how to extract the dynamics in the wavenumber space for systems with the boundaries. Furthermore, we also observe that connectivity of the SPERs changes depending on the fiction, which is analogous to the Lifshitz transition of electron systems.

cond-mat.str-el↗

arXiv2021

Bulk-edge correspondence with generalized chiral symmetry

The bulk-edge correspondence in topological phases is extended to systems with the generalized chiral symmetry, where the conventional chiral symmetry is broken. In such systems, we find that the edge state exhibits an unconventional behavior in the presence of the symmetry breaking by the mass, which is explored explicitly in the case of a deformed Su-Schrieffer-Heeger model. The localization length of the edge states diverges at a certain critical mass, where the edge state touches to the bulk band. The edge state is specified by an imaginary wave vector that becomes real at the touching energy.

cond-mat.str-el↗

arXiv2021

Multiple quantum scar states and emergent slow-thermalization in the flat-band system

Quantum many-body scars (QMBS) appear in a flat-band model with interactions on the saw-tooth lattice. The flat-band model includes a compact support localized eigenstates, called compact localized state (CLS). Some characteristic many-body states can be constructed from the CLSs at a low-filling on the flat-band. These many-body states are degenerate. Starting with such degenerate states we concretely show how to construct multiple QMBSs with different eigenenergies embedded in the entire spectrum. If the degeneracy is lifted by introducing hopping modulation or weak perturbations, these states lifted by these ways can be viewed as multiple QMBSs. In this work, we focus on the study of the perturbation-induced QMBS. Perturbed states, which are connected to the exact QMBSs in the unperturbed limit, indicate common properties of conventional QMBS systems, that is, a subspace with sub-volume or area law scaling entanglement entropy, which indicates the violation of the strong eigenstate thermalization hypothesis (ETH). Also for a specific initial state, slow-thermalization dynamics appears. We numerically demonstrate these subjects. The flat-band model with interactions is a characteristic example in non-integrable systems with the violation of the strong ETH and the QMBS.

cond-mat.stat-mech↗

arXiv2021

Revisiting Flat bands and localization

Flat bands imply lack of itinerancy due to some constraints that, in principle, results in anomalous behaviors with randomness. By a molecular orbital (MO) representation of the flat band systems, random MO models are introduced where the degeneracy due to the flat bands is preserved even with randomness. The zero modes of the chiral symmetric system with sublattice imbalance belong to the class. After explaining the generic flat band construction by MOs, several examples are discussed with numerical demonstration as sawtooth lattice in one dimension and hyper-Pyrochlore lattice in any $d$-dimensions that extends the Kagome ($d=2$) and Pyrochlore ($d=3$) lattices to general dimensions.

cond-mat.dis-nn↗

arXiv2021

Square-root topological phase with time-reversal and particle-hole symmetry

Square-root topological phases have been discussed mainly for systems with chiral symmetry. In this paper, we analyze the topology of the squared Hamiltonian for systems preserving the time-reversal and particle-hole symmetry. Our analysis elucidates that two-dimensional systems of class CII host helical edge states due to the nontrivial topology of the squared Hamiltonian in contrast to the absence of ordinary topological phases. The emergence of the helical edge modes is demonstrated by analyzing a toy model. We also show the emergence of surface states induced by the non-trivial topology of the squared Hamiltonian in three dimensions.

cond-mat.mes-hall↗

arXiv2021

Machine learning of mirror skin effects in the presence of disorder

Non-Hermitian systems with mirror symmetry may exhibit mirror skin effect which is the extreme sensitivity of the spectrum and eigenstates on the boundary condition due to the non-Hermitian topology protected by mirror symmetry. In this paper, we report that the mirror skin effect survives even against disorder which breaks the mirror symmetry. Specifically, we demonstrate the robustness of the skin effect by employing the neural network which systematically predicts the presence/absence of the skin modes, a large number of localized states around the edge. The trained neural network detects skin effects in high accuracy, which allows us to obtain the phase diagram. We also calculate the probability by the neural network for each of states. The above results are also confirmed by calculating the inverse participation ratio.

cond-mat.mes-hall↗

arXiv2021

Square-root topological semimetals

We propose topological semimetals generated by the square-root operation for tight-binding models in two and three dimensions, which we call square-root topological semimetals. The square-root topological semimetals host topological band touching at finite energies, whose topological protection is inherited from the squared Hamiltonian. Such a topological character is also reflected in emergence of boundary modes with finite energies. Specifically, focusing on topological properties of squared Hamiltonian in class AIII, we reveal that a decorated honeycomb (decorated diamond) model hosts finite-energy Dirac cones (nodal lines). We also propose a realization of a square-root topological semimetal in a spring-mass model, where robustness of finite-energy Dirac points against the change of tension is elucidated.

cond-mat.mes-hall↗

arXiv2021

Detecting Bulk Topology of Quadrupolar Phase from Quench Dynamics

Direct measurement of a bulk topological observable in topological phase of matter has been a long-standing issue. Recently, detection of bulk topology through quench dynamics has attracted growing interests. Here, we propose that topological characters of a quantum quadrupole insulator can be read out by quench dynamics. Specifically, we introduce a quantity, a quadrupole moment weighted by the eigenvalues of the chiral operator, which takes zero for the trivial phase and finite for the quadrupolar topological phase. By utilizing an efficient numerical method to track the unitary time evolution, we elucidate that the quantity we propose indeed serves as an indicator of topological character for both noninteracting and interacting cases. The robustness against disorders is also demonstrated.

cond-mat.mes-hall↗

arXiv2021

Robust Zero Modes in Disordered Two-Dimensional Honeycomb Lattice with Kekulé Bond Ordering

Robustness of zero-modes of two-dimensional Dirac fermions is examined numerically for the honeycomb lattice in the presence of Kekulé bond ordering. The split $n=0$ Landau levels in a magnetic field as well as the zero-modes generated by topological defects in the Kekulé ordering are shown to exhibit anomalous robustness against disorder when the chiral symmetry is respected.

cond-mat.dis-nn↗

arXiv2020

Bulk-edge correspondence of classical diffusion phenomena

We elucidate that the diffusive systems, which are widely found in nature, can be a new platform of the bulk-edge correspondence, a representative topological phenomenon. Using a discretized diffusion equation, we demonstrate the emergence of robust edge states protected by the winding number for one- and two-dimensional systems. These topological edge states can be experimentally accessible by measuring the diffusive dynamics at the edges. Furthermore, we discover a novel diffusive phenomenon by numerically simulating the distribution of temperatures for a honeycomb lattice system; the temperature field with wavenumber $π$ cannot diffuse to the bulk, which is attributed to the complete localization of the edge state.

cond-mat.mes-hall↗

arXiv2020

Flat Band Quantum Scar

We show that a quantum scar state, an atypical eigenstate breaking eigenstate thermalization hypothesis embedded in a many-body energy spectrum, can be constructed in flat band systems. The key idea of our construction is to make use of orthogonal compact localized states. We concretely discuss our construction scheme, taking a saw-tooth flat lattice system as an example, and numerically demonstrate the presence of a quantum scar state. Examples of higher-dimensional systems are also addressed. Our construction method of quantum scar has broad applications to various flat band systems.

cond-mat.quant-gas↗

arXiv2020

Systematic construction of topological flat-band models by molecular-orbital representation

On the basis of the "molecular-orbital" representation which describes generic flat-band models, we propose a systematic way to construct a class of flat-band models with finite-range hoppings that have topological natures. In these models, the topological natures are encoded not into the flat band itself but into the dispersive bands touching the flat band. Such a band structure may become a source of exotic phenomena arising from the combination of flat bands, topology and correlations.

cond-mat.mes-hall↗

arXiv2020

Type-III Dirac Cones from Degenerate Directionally Flat Bands: Viewpoint from Molecular-Orbital Representation

We present a systematic method of creating type-III Dirac cones from degenerate directionally flat bands. Here, the directionally flat band means a completely dispersionless band only in a certain direction. The key strategy is to retain one of the directionally flat bands while making the other dispersive, by adding a perturbation having a selected form of a Hamiltonian matrix. Such a form of a perturbation is found by using the "molecular-orbital representation" which we have developed to describe flat-band models. The models thus obtained host type-III Dirac cones even without fine-tuning hopping parameters. To demonstrate the ubiquity of this method, we study concrete examples of two-band models and a four-band model.

cond-mat.mes-hall↗

arXiv2020

Interaction induced doublons and embedded topological subspace in a complete flat-band system

In this work, we investigate effects of weak interactions on a bosonic complete flat-band system. By employing a band projection method, the flat-band Hamiltonian with weak interactions is mapped to an effective Hamiltonian. The effective Hamiltonian indicates that doublons behave as well-defined quasi-particles, which acquire itinerancy through the hopping induced by interactions. When we focus on a two-particle system, from the effective Hamiltonian, an effective subspace spanned only by doublon bases emerges. The effective subspace induces spreading of a single doublon and we find an interesting property: The dynamics of a single doublon keeps short-range density-density correlation in sharp contrast to a conventional two-particle spreading. Furthermore, when introducing a modulated weak interaction, we find an interaction induced topological subspace embedded in the full Hilbert space. We elucidate the embedded topological subspace by observing the dynamics of a single doublon, and show that the embedded topological subspace possesses a bulk topological invariant. We further expect that for the system with open boundary the embedded topological subspace has an interaction induced topological edge mode described by the doublon. The bulk--edge--correspondence holds even for the embedded topological subspace.

cond-mat.quant-gas↗

arXiv2020

Adiabatic Heuristic Principle on a Torus and Generalized Streda Formula

Although the adiabatic heuristic argument of the fractional quantum Hall states has been successful, continuous modification of the flux/statistics of anyons is strictly prohibited due to algebraic constrains of the braid group on a torus. We have numerically shown that the adiabatic heuristic principle for anyons is still valid even though the Hamiltonians cannot be modified continuously. The Chern number of the ground state multiplet is the adiabatic invariant, while the number of the topological degeneracy behaves wildly. A generalized Streda formula is proposed that explains the degeneracy pattern. Nambu-Goldston modes associated with the anyon superconductivity are also suggested numerically.

cond-mat.str-el↗

arXiv2020

Fate of fractional quantum Hall states in open quantum systems: characterization of correlated topological states for the full Liouvillian

Despite previous extensive analysis of open quantum systems described by the Lindblad equation, it is unclear whether correlated topological states, such as fractional quantum Hall states, are maintained even in the presence of the jump term. In this paper, we introduce the pseudo-spin Chern number of the Liouvillian which is computed by twisting the boundary conditions only for one of the subspaces of the doubled Hilbert space. The existence of such a topological invariant elucidates that the topological properties remain unchanged even in the presence of the jump term which does not close the gap of the effective non-Hermitian Hamiltonian (obtained by neglecting the jump term). In other words, the topological properties are encoded into an effective non-Hermitian Hamiltonian rather than the full Liouvillian. This is particularly useful when the jump term can be written as a strictly block-upper (-lower) triangular matrix in the doubled Hilbert space, in which case the presence or absence of the jump term does not affect the spectrum of the Liouvillian. With the pseudo-spin Chern number, we address the characterization of fractional quantum Hall states with two-body loss but without gain, elucidating that the topology of the non-Hermitian fractional quantum Hall states is preserved even in the presence of the jump term. This numerical result also supports the use of the non-Hermitian Hamiltonian which significantly reduces the numerical cost. Similar topological invariants can be extended to treat correlated topological states for other spatial dimensions and symmetry (e.g., one-dimensional open quantum systems with inversion symmetry), indicating the high versatility of our approach.

cond-mat.mes-hall↗

arXiv2020

Interaction Induced Topological Charge Pump

Based on a topological transition of the symmetry protected topological phase (SPT), an interaction induced topological charge pump (iTCP) is proposed with the symmetry breaking parameter as a synthetic dimension. It implies that the phase boundary of the SPT is the topological obstruction although iTCP and the gap closing singularity is stable for symmetry breaking perturbations. We have confirmed the bulk-edge correspondence for this iTCP using DMRG for the Rice-Mele model with nearest-neighbor interactions. As for a realization in optical lattices, an interaction sweeping pump protocol is proposed as well.

cond-mat.quant-gas↗