arXiv subjects

Tomonari Mizoguchi

Publications and source records attributed to Tomonari Mizoguchi.

At least 37 records · Page 2Linked to original sources

arXiv2022

Square-root higher-order topological insulator on a decorated honeycomb lattice

Square-root topological insulators are recently-proposed intriguing topological insulators, where the topologically nontrivial nature of Bloch wave functions is inherited from the square of the Hamiltonian. In this paper, we propose that higher-order topological insulators can also have their square-root descendants, which we term square-root higher-order topological insulators. There, emergence of in-gap corner states is inherited from the squared Hamiltonian which hosts higher-order topology. As an example of such systems, we investigate the tight-binding model on a decorated honeycomb lattice, whose squared Hamiltonian includes a breathing kagome-lattice model, a well-known example of higher-order topological insulators. We show that the in-gap corner states appear at finite energies, which coincides with the non-trivial bulk polarization. We further show that the existence of in-gap corner states results in characteristic single-particle dynamics, namely, setting the initial state to be localized at the corner, the particle stays at the corner even after a long time. Such characteristic dynamics may experimentally be detectable in photonic crystals.

cond-mat.mes-hall↗

arXiv2022

Competition of First-Order and Second-Order Topology on the Honeycomb Lattice

We investigate both first-order topology, as realized through Haldane's model, and second-order topology, implemented through an additional Kekulé-distortion, on the honeycomb lattice. The interplay and competition of both terms result in a phase diagram at half-filling which contains twelve distinct phases. All phases can be characterized by the first Chern number or by a quantized $\mathbb{Z}_Q$ Berry phase. Highlights include phases with high Chern numbers, a novel $\mathbb{Z}_6$ topological phase, but also coupled kagome-lattice Chern insulators. Furthermore, we explore the insulating phases at lower fillings, and find again first-order and second-order topological phases. Finally, we identify real-space structures which feature corner states not only at half but also at third and sixth fillings, in agreement with the quantized $\mathbb{Z}_Q$ Berry phases.

cond-mat.mes-hall↗

arXiv2022

Non-Hermitian topology in rock-paper-scissors games

Non-Hermitian topology is a recent hot topic in condensed matters. In this paper, we propose a novel platform drawing interdisciplinary attention: rock-paper-scissors (RPS) cycles described by the evolutionary game theory. Specifically, we demonstrate the emergence of an exceptional point and a skin effect by analyzing topological properties of their payoff matrix. Furthermore, we discover striking dynamical properties in an RPS chain: the directive propagation of the population density in the bulk and the enhancement of the population density only around the right edge. Our results open new avenues of the non-Hermitian topology and the evolutionary game theory.

physics.soc-ph↗

arXiv2021

Chiral edge modes in evolutionary game theory: a kagome network of rock-paper-scissors

We theoretically demonstrate the realization of a chiral edge mode in a system beyond natural science. Specifically, we elucidate that a kagome network of rock-paper-scissors (K-RPS) hosts a chiral edge mode of the population density which is protected by the non-trivial topology in the bulk. The emergence of the chiral edge mode is demonstrated by numerically solving the Lotka-Volterra (LV) equation. This numerical result can be intuitively understood in terms of cyclic motion of a single RPS cycle which is analogues to the cyclotron motion of fermions. Furthermore, we point out that a linearized LV equation is mathematically equivalent to the Schrödinger equation describing quantum systems. This equivalence allows us to clarify the topological origin of the chiral edge mode in the K-RPS; a non-zero Chern number of the payoff matrix induces the chiral edge mode of the population density, which exemplifies the bulk-edge correspondence in two-dimensional systems described by evolutionary game theory.

cond-mat.mes-hall↗

arXiv2021

Flat-band solutions in $D$-dimensional decorated diamond and pyrochlore lattices: Reduction to molecular problem

Flat-band models have been of particular interest from both fundamental aspects and realization in materials. Beyond the canonical examples such as Lieb lattices and line graphs, a variety of tight-binding models are found to possess flat bands. However, analytical treatment of dispersion relations is limited, especially when there are multiple flat bands with different energies. In this paper, we present how to determine flat-band energies and wave functions in tight-binding models on decorated diamond and pyrochlore lattices in generic dimensions $D \geq 2$. For two and three dimensions, such lattice structures are relevant to various organic and inorganic materials, and thus our method will be useful to analyze the band structures of these materials.

cond-mat.mtrl-sci↗

arXiv2021

Flat band, spin-1 Dirac cone, and Hofstadter diagram in the fermionic square kagome model

We study characteristic band structures of the fermions on a square kagome lattice, one of the two-dimensional lattices hosting a corner-sharing network of triangles. We show that the band structures of the nearest-neighbor tight-binding model exhibit many characteristic features, including a flat band which is ubiquitous among frustrated lattices. On the flat band, we elucidate its origin by using the molecular-orbital representation and also find localized exact eigenstates called compact localized states. In addition to the flat band, we also find two spin-1 Dirac cones with different energies. These spin-1 Dirac cones are not described by the simplest effective Dirac Hamiltonian because the middle band is bended and the energy spectrum is particle-hole asymmetric. We also investigated the Hofstadter problem on a square kagome lattice in the presence of an external field and find that the profile of the Chern numbers around the modified spin-1 Dirac cones coincides with the conventional one.

cond-mat.mes-hall↗

arXiv2021

Bulk-edge correspondence in two-dimensional topological semimetals: A transfer matrix study of antichiral edge modes

We study edge modes in topological semimetals which have an energy band structure of ordinary semimetals but can be characterized by a Chern number. More specifically, we focus on a Qi-Wu-Zhang-type square-lattice model and a Haldane-type honeycomb model, both of which exhibit antichiral edge modes whose wave packets propagate in the same direction at both parallel edges of the strip. To obtain these analytical solutions of the edge modes, we apply the transfer matrix method which was developed in the previous work [Phys. Rev. B \textbf{101}, 014442 (2020)]. As a result, we show that the bulk-edge correspondence is broken down for a certain range of the model parameters. More precisely, when increasing the strength of a hopping amplitude of the Qi-Wu-Zhang-type model, the edge modes abruptly disappear, although the non-trivial Chern number does not change. In the Haldane-type model, for varying the model parameters, the edge modes do not necessarily disappear, and the non-trivial Chern number does not change. However, the energy spectral flows of the edge modes from the valence band to the conduction band are abruptly broken at a certain set of the model parameters.

cond-mat.mes-hall↗

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

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

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↗

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

Topological Modes Protected by Chiral and Two-Fold Rotational Symmetry in a Spring-Mass Model with a Lieb Lattice Structure

We propose how to realize the topological modes, which correspond to topological zero modes for a quantum system, protected by chiral and rotation symmetry for a mechanical system. Specifically, we show the emergence of topological modes protected by chiral and two-fold rotational symmetry by a spring-mass system with a Lieb lattice structure and dents on the floor. Moreover, comparing the results of a tight-binding model, we have found the additional topological modes for our spring-mass model due to the extra degrees of freedoms. Our approach to realize the topological modes can be applied to other cases with rotation symmetry, e.g., a system of a honeycomb lattice with three-fold rotational symmetry.

cond-mat.mes-hall↗

arXiv2020

Mirror skin effect and its electric circuit simulation

We analyze impacts of crystalline symmetry on the non-Hermitian skin effects. Focusing on mirror symmetry, we propose a novel type of skin effects, a mirror skin effect, which results in significant dependence of energy spectrum on the boundary condition only for the mirror invariant line in the two-dimensional Brillouin zone. This effect arises from the topological properties characterized by a mirror winding number. We further reveal that the mirror skin effect can be observed for an electric circuit composed of negative impedance converters with current inversion where switching the boundary condition significantly changes the admittance eigenvalues only along the mirror invariant lines. Furthermore, we demonstrate that extensive localization of the eigenstates for each mirror sector result in an anomalous voltage response.

cond-mat.mes-hall↗

arXiv2020

Field-selective classical spin liquid and magnetization plateaus on kagome lattice

We obtain a classical spin liquid (CSL) phase by applying a magnetic field in $J_1$-$J_2$-$J_3$ Ising model on a kagome lattice. As we proved in the previous study [Phys. Rev. Lett. {\bf 119}, 077207 (2017)], this model realizes one species of CSL, the hexamer CSL, at zero magnetic field, which consists of macroscopically degenerate spin configurations with mixed total magnetization, $M$. The magnetic field selects its subset, which can be mapped to a trimer covering of the dual lattice, and forms a magnetization plateau of $M=1/9$. In addition to this CSL, we find two other magnetization plateaus at $M=5/9$ and $17/27$, which are ascribed to the "multimer" superstructures on a dual lattice.

cond-mat.str-el↗