arXiv subjects

Yasuhiro Hatsugai

Publications and source records attributed to Yasuhiro Hatsugai.

At least 73 records · Page 4Linked to original sources

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

Higher-order topological phases in a spring-mass model on a breathing kagome lattice

We propose a realization of higher-order topological phases in a spring-mass model with a breathing kagome structure. To demonstrate the existence of the higher-order topological phases, we characterize the topological properties and show that the corner states appear under the fixed boundary condition. To characterize the topological properties, we introduce a formula for the $\mathbb{Z}_3$ Berry phases in the Brillouin zone. From the numerical result of this $\mathbb{Z}_3$ Berry phase, we have elucidated that coupling between the longitudinal and transverse modes yields a state characterized by the Berry phase $\frac{2π}{3}$ for our mechanical breathing kagome model. In addition, we suggest that the corner states can be detected experimentally through a forced vibration.

cond-mat.mes-hall↗

arXiv2020

Exceptional band touching for strongly correlated systems in equilibrium

Quasi-particles described by Green's functions of equilibrium systems exhibit non-Hermitian topological phenomena because of their finite lifetime. This non-Hermitian perspective on equilibrium systems provides new insights into correlated systems and attracts much interest because of its potential to solve open questions in correlated compounds. In this paper, we provide a concise review of the non-Hermitian topological band structures for quantum many-body systems in equilibrium as well as their classification.

cond-mat.str-el↗

arXiv2019

Flat bands and higher-order topology in polymerized triptycene: Tight-binding analysis on decorated star lattices

In a class of carbon-based materials called polymerized triptycene, which consist of triptycene molecules and phenyls, exotic electronic structures such as Dirac cones and flat bands arise from the kagome-type network. In this paper, we theoretically investigate the tight-binding models for polymerized triptycene, focusing on the origin of flat bands and the topological properties. The mechanism of the existence of the flat bands is elucidated by using the "molecular-orbital" representation, which we have developed in the prior works. Further, we propose that the present material is a promising candidate to realize the two-dimensional second-order topological insulator, which is characterized by the boundary states localized at the corners of the sample. To be concrete, we propose two methods to realize the second-order topological insulator, and elucidate the topological properties of the corresponding models by calculating the corner states as well as the bulk topological invariant, namely the $\mathbb{Z}_3$ Berry phase.

cond-mat.mes-hall↗

arXiv2019

Higher-order Topological Mott Insulators

We propose a new correlated topological state which we call a higher-order topological Mott insulator (HOTMI). This state exhibits a striking bulk-boundary correspondence due to electron correlations. Namely, the topological properties in the bulk, characterized by the Z3 spin-Berry phase, result in gapless corner modes emerging only in spin excitations (i.e., the single-particle excitations remain gapped around the corner). We demonstrate the emergence of the HOTMI in a Hubbard model on the kagome lattice, and elucidate how strong correlations change gapless corner modes at the noninteracting case.

cond-mat.str-el↗

arXiv2019

$\mathbb{Z}_Q$ Berry Phase for Higher-Order Symmetry-Protected Topological Phases

We propose the $\mathbb{Z}_Q$ Berry phase as a topological invariant for higher-order symmetry-protected topological (HOSPT) phases for two- and three-dimensional systems. It is topologically stable for electron-electron interactions assuming the gap remains open. As a concrete example, we show that the Berry phase is quantized in $\mathbb{Z}_4$ and characterizes the HOSPT phase of the extended Benalcazar-Bernevig-Hughes (BBH) model, which contains the next-nearest neighbor hopping and the intersite Coulomb interactions. In addition, we introduce the $\mathbb{Z}_4$ Berry phase for the spin-model-analog of the BBH model, whose topological invariant has not been found so far. Furthermore, we demonstrate the Berry phase is quantized in $\mathbb{Z}_4$ for the three-dimensional version of the BBH model. We also confirm the bulk-corner correspondence between the $\mathbb{Z}_4$ Berry phase and the corner states in the HOSPT phases.

cond-mat.str-el↗

arXiv2019

Molecular-orbital representation of generic flat-band models

We develop a framework to describe a wide class of flat-band models, with and without a translational symmetry, by using "molecular orbitals" introduced in the prior work (HATSUGAI Y. and MARUYAMA I., \textit{EPL}, \textbf{95}, (2011) 20003). Using the molecular-orbital representation, we shed new light on the band-touching problem between flat and dispersive bands. We show that the band touching occurs as a result of collapse, or the linearly dependent nature, of molecular orbitals. Conversely, we can gap out the flat bands by modulating the molecular orbitals so that they do not collapse, which provides a simple prescription to construct models having a finite energy gap between flat bands and dispersive bands.

cond-mat.mes-hall↗

arXiv2019

Higher-Order Topological Phase in a Honeycomb-Lattice Model with Anti-Kekulé Distortion

Higher-order topological insulators have attracted considerable interests as a novel topological phase of matter, where topologically non-trivial nature of bulk protects boundary states whose co-dimension is larger than one. It has been revealed that the alternating pattern of hopping amplitudes in two-dimensional lattices provides a promising route to realization of the higher-order topological insulators. In this paper, we propose that a honeycomb-lattice model with anti-Kekulé distortion hosts a higher-order topological phase. Here, the term anti-Kekulé distortion means that the pattern of strong and weak hoppings is opposite to that for the conventional Kekulé distortion. We demonstrate the existence of the higher-order topological phase by calculating the $\mathbb{Z}_6$ Berry phase that serves as a bulk topological invariant of the higher-order topological phase, and by showing the existence of corner states.

cond-mat.mes-hall↗

arXiv2019

Sequential quantum phase transitions in $J_1$-$J_2$ Heisenberg chains with integer spins ($S > 1$): Quantized Berry phase and valence-bond solids

On the basis of a Berry-phase analysis, we study the ground state of the $J_1$-$J_2$ Heisenberg chain for $S=2,3,4$. We find that changes of the Berry phase occur $S$ times for spin-$S$ systems, indicating the sequential phase transitions. The sequential phase transitions are associated with the change of valence-bond configurations of the ground states. To demonstrate this numerically, we connect the $J_1$-$J_2$ Heisenberg Hamiltonian with the generalized Affleck-Kennedy-Lieb-Tasaki model, and show that the different phases are connected to the different valence-bond-solid states.

cond-mat.str-el↗

arXiv2019

Non-Hermitian fractional quantum Hall states

We demonstrate the emergence of a topological ordered phase for non-Hermitian systems. Specifically, we elucidate that systems with non-Hermitian two-body interactions show a fractional quantum Hall (FQH) state. The non-Hermitian Hamiltonian is considered to be relevant to cold atoms with dissipation. We conclude the emergence of the non-Hermitian FQH state by the presence of the topological degeneracy and by the many-body Chern number for the ground state multiplet showing $C_{\mathrm{tot}}=1$. The robust topological degeneracy against non-Hermiticity arises from the many-body translational symmetry. Furthermore, we discover that the FQH state emerges without any repulsive interactions, which is attributed to a phenomenon reminiscent of the continuous quantum Zeno effect.

cond-mat.mes-hall↗

arXiv2019

Exceptional rings protected by emergent symmetry for mechanical systems

We propose mechanical systems, described by Newton's equation of motion, as suited platforms for symmetry protection of non-Hermitian topological degeneracies. We point out that systems possess emergent symmetry, which is a unique properties of mechanical systems. Because of the emergent symmetry, in contrast to other systems, fine-tuning of parameters (e.g., gain and loss) is not required to preserve the symmetry protecting exceptional rings in two dimensions. The presence of symmetry-protected exceptional rings (SPERs) in two dimensions is numerically demonstrated for a mechanical graphene with friction. Furthermore, classification of symmetry-protected non-Hermitian degeneracies is addressed by taking into account the above special characteristics of mechanical systems.

cond-mat.mes-hall↗

arXiv2019

Topologically Protected Doubling of Tilted Dirac Fermions in Two Dimensions

The doubling of massless Dirac fermions on two-dimensional lattices is theoretically studied. It has been shown that the doubling of massless Dirac fermions on a lattice with broken chiral symmetry is topologically protected even when the Dirac cone is tilted. This is due to the generalized chiral symmetry defined for lattice systems, where such models can be generated by a deformation of the chiral-symmetric lattice models. The present paper shows for two-band lattice models that this is a general way to produce systems with the generalized chiral symmetry in that such systems can always be transformed back to a lattice model with the conventional chiral symmetry. We specifically show that the number of zero modes is an invariant of the transformation, leading to the topological protection à la Nielsen-Ninomiya of the doubling of tilted and massless Dirac fermions in two dimensions.

cond-mat.mes-hall↗

arXiv2019

Many-body Chern number without integration

The celebrated work of Niu, Thouless, and Wu demonstrated the quantization of Hall conductance in the presence of many-body interactions by revealing the many-body counterpart of the Chern number. The generalized Chern number is formulated in terms of the twisted angles of the boundary condition, instead of the single particle momentum, and involves an integration over all possible twisted angles. However, this formulation is physically unnatural, since topological invariants directly related to observables should be defined for each Hamiltonian under a fixed boundary condition. In this work, we show via numerical calculations that the integration is indeed unnecessary - the integrand itself is effectively quantized and the error decays exponentially with the system size. This implies that the numerical cost in computing the many-body Chern number could, in principle, be significantly reduced as it suffices to compute the Berry connection for a single value of the twisted boundary condition if the system size is sufficiently large.

cond-mat.str-el↗

arXiv2019

Fractionally quantized Berry's phase in an anisotropic magnet on the Kagome lattice

A fractionally quantized Berry phase is examined numerically in an anisotropic spin-1/2 XXZ model on the Kagome lattice. It is shown that the Berry phase has a fractionally quantized and non-zero value when an anisotropy is increased, which is consistent with the emergence of the tripartite entangled plaquette phase discussed by J. Carrasquilla et al. [Phys. Rev. B96, 054405 (2017)].

cond-mat.stat-mech↗

arXiv2019

Phase diagram of disordered higher-order topological insulator: A machine learning study

A higher-order topological insulator is a new concept of topological states of matter, which is characterized by the emergent boundary states whose dimensionality is lower by more than two compared with that of the bulk, and draws a considerable interest. Yet, its robustness against disorders is still unclear. Here we investigate a phase diagram of higher-order topological insulator phases in a breathing kagome model in the presence of disorders, by using a state-of-the-art machine learning technique. We find that the corner states survive against the finite strength of disorder potential as long as the energy gap is not closed, indicating the stability of the higher-order topological phases against the disorders.

cond-mat.dis-nn↗

arXiv2019

Weyl points of mechanical diamond

A spring-mass model arranged in a diamond structure --- mechanical diamond --- is analyzed in terms of topology in detail. We find that, additional springs connecting the next-nearest-neighbor pairs of mass points and the modulation of the mass parameters to the pristine mechanical diamond generates multiple pairs of Weyl points in the frequency dispersion. Evolution of the Weyl point positions in the Brillouin zone against the uniform outward tension is tracked and explained by the point group symmetry, especially tetrahedral symmetry of the NNN springs. Interestingly, there happens a rapid transmutation of the monopole charges of the Weyl points as the tension varies. We also show surface Fermi arcs in the case with anisotropy in the NNN springs.

cond-mat.mes-hall↗

arXiv2018

Exceptional rings in two-dimensional correlated systems with chiral symmetry

Emergence of exceptional points in two dimensions is one of the remarkable phenomena in non-Hermitian systems. We here elucidate the impacts of symmetry on the non-Hermitian physics. Specifically, we analyze chiral symmetric correlated systems in equilibrium where the non-Hermitian phenomena are induced by the finite lifetime of quasi-particles. Intriguingly, our analysis reveals that the combination of symmetry and non-Hermiticity results in novel topological degeneracies of energy bands which we call symmetry-protected exceptional rings (SPERs). We observe the emergence of SPERs by analyzing a non-Hermitian Dirac Hamiltonian. Furthermore, by employing the dynamical mean-field theory, we demonstrate the emergence of SPERs in a correlated honeycomb lattice model whose single-particle spectrum is described by a non-Hermitian Dirac Hamiltonian. We uncover that the SPERs survive even beyond the non-Hermitian Dirac Hamiltonian, which is related to a zero-th Chern number.

cond-mat.str-el↗