arXiv subjects

Norio Kawakami

Publications and source records attributed to Norio Kawakami.

At least 37 records · Page 2Linked to original sources

arXiv2020

Bulk-edge correspondence in nonunitary Floquet systems with chiral symmetry

We study topological phases in one-dimensional open Floquet systems driven by chiral symmetric nonunitary time evolution. We derive a procedure to calculate topological numbers from nonunitary time-evolution operators with chiral symmetry. While the procedure has been applied to open Floquet systems described by nonunitary time-evolution operators, we give the microscopic foundation and clarify its validity for the first time. We construct a model of chiral symmetric nonunitary quantum walks classified into class BDI$^\dagger$ or AIII, which is one of enlarged symmetry classes for topological phases in open systems, based on experiments of discrete-time quantum walks. Then, we confirm that the topological numbers obtained from the derived procedure give correct predictions of the emergent edge states. We also show that the model retains $\mathcal{PT}$ symmetry in certain cases and its dynamics is crucially affected by the presence or absence of $\mathcal{PT}$ symmetry.

cond-mat.mes-hall↗

arXiv2020

Rectification in Nonequilibrium Steady States of Open Many-Body Systems

We study how translationally invariant couplings of many-particle systems and nonequilibrium baths can be used to rectify particle currents, for which we consider minimal setups to realize bath-induced currents in nonequilibrium steady states of one-dimensional open fermionic systems. We first analyze dissipative dynamics associated with a nonreciprocal Lindblad operator and identify a class of Lindblad operators that are sufficient to acquire a unidirectional current. We show that unidirectional particle transport can in general occur when a Lindblad operator is reciprocal provided that the inversion symmetry and the time-reversal symmetry of the microscopic Hamiltonian are broken. We demonstrate this mechanism on the basis of both analytical and numerical approaches including the Rashba spin-orbit coupling and the Zeeman magnetic field.

cond-mat.quant-gas↗

arXiv2020

Two-Dimensional Thouless Pumping of Ultracold Fermions in Obliquely Introduced Optical Superlattice

We propose a two-dimensional (2D) version of Thouless pumping that can be realized by using ultracold atoms in optical lattices. To be specific, we consider a 2D square lattice tight-binding model with an obliquely introduced superlattice. It is demonstrated that quantized particle transport occurs in this system, and that the transport is expressed as a solution of a Diophantine equation. This topological nature can be understood by mapping the Hamiltonian to a three-dimensional (3D) cubic lattice model with a homogeneous magnetic field. We also propose a continuum model with obliquely introduced superlattice and obtain the amount of pumping by calculating the Berry curvature. For this model, the same Diophantine equation can be derived from the plane-wave approximation. Furthermore, we investigate the effect of a harmonic trap by solving the time-dependent Schrödinger equation. Under a harmonic trap potential, as often used in cold atom experiments, we show, by numerical simulations, that nearly quantized pumping occurs when the phase of the superlattice potential is driven at a moderate speed. Also, we find that two regions appear, the Hofstadter region and the rectifying region, depending on the modulation amplitude of the superlattice potential. In the rectifying region with larger modulation amplitudes, we uncover that the pumping direction is restricted to exactly the $x$-axis or the $y$-axis direction. This difference in these two regions causes a crossover behavior, characterizing the effect of the harmonic trap.

cond-mat.quant-gas↗

arXiv2020

Exact Floquet quantum many-body scars under Rydberg blockade

Quantum many-body scars have attracted much interest as a violation of the eigenstate thermalization hypothesis (ETH) due to recent experimental observation in Rydberg atoms and related theoretical studies. In this paper, we construct a model hosting exact Floquet quantum many-body scars, which violate the Floquet version of ETH. We consider two uniformly-driven static Hamiltonians prohibiting neighboring up spins (Rydberg blockade) like the PXP model, and construct a binary drive composed of them. We show that there exists a four-dimensional subspace which completely avoids thermalization to infinite temperature and that any other states, including some special scar states reported in the static PXP model, are vulnerable to heating and relax to infinite temperature. We also construct a more generalized periodic drive composed of time-dependent PXP-type Hamiltonians showing exact Floquet quantum many-body scars and discuss possible experimental realization of the model in Rydberg atoms.

cond-mat.stat-mech↗

arXiv2020

Stability of topologically protected edge states in nonlinear quantum walks: Additional bifurcations unique to Floquet systems

Recently, effects of nonlinearity on topologically nontrivial systems have attracted attention and the stability of topologically protected edge states has been studied for a quantum walk with nonlinear effects, which is akin to time-periodically driven systems (Floquet systems). In the previous work, it has been found that the edge states can be stable attractors or unstable repellers depending on their intrinsic topological property, while the stability is not affected by the strength of nonlinearity. In the present work, we find additional bifurcations at which edge states change from stable attractors to unstable repellers with increasing the strength of nonlinearity in nonlinear quantum walks, for the first time. The new bifurcations are unique to Floquet systems, since we take dynamical properties of Floquet systems into consideration by directly applying the time-evolution operator of the quantum walks to the linear stability analysis. Our results shed new light on nonlinear effects on topological edge states in Floquet systems.

quant-ph↗

arXiv2020

Bulk-edge correspondence and stability of multiple edge states of a $\mathcal{PT}$ symmetric non-Hermitian system by using non-unitary quantum walks

Topological phases and the associated multiple edge states are studied for parity and time-reversal $(\mathcal{PT})$ symmetric non-Hermitian open quantum systems by constructing a non-unitary three-step quantum walk retaining $\mathcal{PT}$ symmetry in one dimension. We show that the non-unitary quantum walk has large topological numbers of the $\mathbb{Z}$ topological phase and numerically confirm that multiple edge states appear as expected from the bulk-edge correspondence. Therefore, the bulk-edge correspondence is valid in this case. Moreover, we study the stability of the multiple edge states against a symmetry-breaking perturbation so that the topological phase is reduced to $\mathbb{Z}_2$ from $\mathbb{Z}$. In this case, we find that the number of edge states does not become one unless a pair of edge states coalesce at an exceptional point. Thereby, this is a new kind of breakdown of the bulk-edge correspondence in non-Hermitian systems. The mechanism of the prolongation of edge states against the symmetry-breaking perturbation is unique to non-Hermitian systems with multiple edge states and anti-linear symmetry. Toward experimental verifications, we propose a procedure to determine the number of multiple edge states from the time evolution of the probability distribution.

quant-ph↗

arXiv2020

Anomalous Hydrodynamic Transport in Interacting Noncentrosymmetric Metals

In highly conductive metals with sufficiently strong momentum-conserving scattering, the electron momentum is regarded as a long-lived quantity, whose dynamics is described by an emergent hydrodynamic theory. In this paper, we develop an electron hydrodynamic theory for noncentrosymmetric metals, where a novel class of electron fluids is realized by lowering crystal symmetries and the resulting geometrical effects. The obtained hydrodynamic equation suggests a nontrivial analogy between electron fluids in noncentrosymmetric metals and chiral fluids in vacuum, and predicts novel hydrodynamic transport phenomena, that is, asymmetric Poiseuille flow and anomalous edge current. Our theory also gives a hydrodynamic description of the counterpart of various anomalous transport phenomena such as the quantum nonlinear Hall effect. Furthermore, we give a symmetry consideration on the hydrodynamic equation and propose several experimental setups to realize such anomalous hydrodynamic transport in the existing hydrodynamic materials, including bilayer graphene and Weyl semimetals.

cond-mat.mes-hall↗

arXiv2020

Dynamical sign reversal of magnetic correlations in dissipative Hubbard models

In quantum magnetism, the virtual exchange of particles mediates an interaction between spins. Here, we show that an inelastic Hubbard interaction fundamentally alters the magnetism of the Hubbard model due to dissipation in spin-exchange processes, leading to sign reversal of magnetic correlations in dissipative quantum dynamics. This mechanism is applicable to both fermionic and bosonic Mott insulators, and can naturally be realized with ultracold atoms undergoing two-body inelastic collisions. The dynamical reversal of magnetic correlations can be detected by using a double-well optical lattice or quantum-gas microscopy, the latter of which facilitates the detection of the magnetic correlations in one-dimensional systems because of spin-charge separation. Our results open a new avenue toward controlling quantum magnetism by dissipation.

cond-mat.quant-gas↗

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

Nonlocal optical responses of ultrapure metals in the hydrodynamic regime

Our conventional understanding of optical responses in metals has been based on the Drude theory. In recent years, however, it has become possible to prepare ultrapure metallic samples where the electron-electron scattering becomes the most dominant process governing transport and thus the Drude theory, where momentum-relaxing scatterings such as electron-impurity scattering are assumed to be dominant, is no longer valid. This regime is called the hydrodynamic regime and described by an emergent hydrodynamic theory. Here, we develop a basic framework of optical responses in the hydrodynamic regime. Based on the hydrodynamic equation, we reveal the existence of a ``hydrodynamic mode'' resulting from the viscosity effect and compute the reflectance and the transmittance in three-dimensional electron fluids. Our theory also describes how to probe the hydrodynamic effects and measure the viscosity through simple optical techniques.

cond-mat.mes-hall↗

arXiv2019

Reflection-Symmetry Protected Antiferromagnetic Topological Insulator in Three-Dimensional Heavy-Fermion Systems

We study the topological properties of an antiferromagnetic phase with reflection symmetry in three-dimensional heavy-fermion systems. We here propose a reflection-symmetric topological state in the three-dimensional antiferromagnetic phase and demonstrate how the paramagnetic phase changes into the antiferromagnetic topological phase of f -electron materials such as SmB6.

cond-mat.str-el↗

arXiv2019

Chiral-symmetry protected exceptional torus in correlated nodal-line semi-metals

We analyze a diamond-lattice Hubbard model with the spatially modulated Hubbard interaction. Our dynamical mean-field analysis with special emphasis on non-Hermitian properties elucidates that the gapless nodal line changes into symmetry-protected exceptional torus (SPET) at the Fermi level enclosing the three-dimensional open Fermi surface, which is unique to non-Hermitian physics with chiral symmetry. Furthermore, we also elucidate the effects of the SPETs on the magnetic response; our results based on the random-phase approximation combined with the the dynamical mean-field theory shows that SPETs enhance the magnetic susceptibility at the weakly correlated sites, exemplifying effects of non-Hermitian degeneracies on responses to external fields.

cond-mat.str-el↗

arXiv2019

Floquet engineering of topological phases protected by emergent symmetries under resonant drives

Floquet engineering is one of the most vigorous fields in periodically driven (Floquet) systems, with which we can control phases of matter usually by high-frequency drives. In this paper, with Floquet engineering by a combination of high-frequency drives and resonant drives, we propose a way to realize nontrivial topological phases protected by a $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry only in the presence of a $\mathbb{Z}_2$ symmetry, using a robust emergent $\mathbb{Z}_2$ symmetry induced by the resonant drives. Moreover, the symmetry protected topological (SPT) phases are switchable between nontrivial and trivial phases only by the direction of a static transverse field, and even perturbations on the resonant drive can be utilized to realize richer SPT phases. We also discuss the real-time dynamics of the model, and find that which topological phases the system lies in can be distinguished by a period doubling of a nonlocal order parameter, as with discrete time crystals. A realization or a control of nontrivial SPT phases without the required symmetries by resonant drives, proposed in this paper, would shed a new light on the observation of topological phenomena in nonequilibrium setups.

cond-mat.mes-hall↗

arXiv2019

Quantum oscillations in strongly correlated topological Kondo insulators

The observation of quantum oscillations in topological Kondo insulators SmB6 and YbB12 is a recent puzzling experimental discovery. Quantum oscillations observed in the resistivity and the magnetization are usually explained by the existence of the Fermi surface. However, Kondo insulators do not have a Fermi surface and thus should not show quantum oscillations. By performing dynamical mean-field calculations for topologically nontrivial Kondo insulators in a magnetic field, we analyze the effect of correlations on the emergence of quantum oscillations in narrow-gap topological Kondo insulators and demonstrate that the interplay between correlations and nonlocal hybridization, ubiquitously occurring in topological Kondo insulators, can lead to observable quantum oscillations without the necessity of a Fermi surface. Particularly, we show that correlations make it easier to observe quantum oscillations in the magnetization and the resistivity of the bulk material. The fundamental mechanism for these quantum oscillations is a combination of correlation effects and Landau levels coming very close to the Fermi energy. We furthermore demonstrate that quantum oscillations in a three-dimensional system can be understood by analyzing the physics on the two-dimensional planes in the momentum space for which the hybridization in direction of the magnetic field vanishes. We believe that this scenario is relevant to understanding the observation of quantum oscillations in the magnetic torque for SmB6 as well as oscillations in the resistivity and the magnetic torque of YbB12.

cond-mat.str-el↗

arXiv2019

High-frequency Expansion for Floquet Prethermal Phases with Emergent Symmetries: Application to Time Crystals and Floquet Engineering

Prethermalization, where quasi-steady states are realized in the intermediate long time regime (prethermal regime), in periodically driven (Floquet) systems is an important phenomenon since it provides a platform of nontrivial Floquet many-body physics. In this Letter, we consider Floquet systems with dual energy scales: the Hamiltonian consists of two different terms whose amplitude is either comparable or much smaller than the frequency. As a result, when the larger-amplitude drive induces a $\mathbb{Z}_N$ symmetry operation, we obtain the effective static Hamiltonian respecting a new emergent $\mathbb{Z}_N$ symmetry in high frequency expansions, which describes the dynamics of such Floquet systems in the prethermal regime. As an application of our formulation, we consider prethermal discrete time crystals, in which our formalism gives a general way to analyze them in the prethermal regime in terms of the static effective Hamiltonian. We also provide an application to Floquet engineering, with which we can perform simultaneous control of phases and symmetries of the systems. This enables us to control symmetry protected topological phases even when the original system does not respect the symmetry.

cond-mat.mes-hall↗

arXiv2019

Theory of Non-Hermitian Fermionic Superfluidity with a Complex-Valued Interaction

Motivated by recent experimental advances in ultracold atoms, we analyze a non-Hermitian (NH) BCS Hamiltonian with a complex-valued interaction arising from inelastic scattering between fermions. We develop a mean-field theory to obtain a NH gap equation for order parameters, which are different from the standard BCS ones due to the inequivalence of left and right eigenstates in the NH physics. We find unconventional phase transitions unique to NH systems: superfluidity shows reentrant behavior with increasing dissipation, as a consequence of non-diagonalizable exceptional points, lines, and surfaces in the quasiparticle Hamiltonian for weak attractive interactions. For strong attractive interactions, the superfluid gap never collapses but is enhanced by dissipation due to an interplay between the BCS-BEC crossover and the quantum Zeno effect. Our results lay the groundwork for studies of fermionic superfluidity subject to inelastic collisions.

cond-mat.quant-gas↗

arXiv2019

Efficient method to compute $\mathbb{Z}_4$-indices with glide symmetry and applications to Möbius materials, $\mathrm{CeNiSn}$ and $\mathrm{UCoGe}$

We propose an efficient method to numerically evaluate $\mathbb{Z}_4$-indices of Möbius/hourglass topological phases with glide symmetry. Our method directly provides $\mathbb{Z}_4$-indices in the lattice Brillouin zone while the existing method requires careful observations of momentum dependent Wannier charge centers. As applications, we perform systematic computation of $\mathbb{Z}_4$-indices for Möbius materials, $\mathrm{CeNiSn}$ and $\mathrm{UCoGe}$. In particular, our analysis elucidates that $\mathrm{UCoGe}$ shows strong Möbius superconductivity for the $A_u$- or $B_{3u}$-representation whose topology has not been fully characterized. Furthermore, obtained phase diagrams reveal novel topological gapless excitations in the bulk which are protected by nonsymmorphic glide symmetry. We observe these gapless excitations with glide symmetry by doping holes into the superconducting phase of the $B_{1u}$- or $B_{3u}$-representation.

cond-mat.str-el↗

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↗