論文 - 早田　智也

Chiral fermion in the Hamiltonian lattice gauge theory

Hayata T., Nakayama K., Yamamoto A.

Physical Review D 108 （ 3 ）  2023年08月

査読有り,  ISSN  24700010

　概要を見る

We discuss the chiral fermion in the Hamiltonian formalism of lattice gauge theory. Although the naive chiral charge operator does not commute with the Hamiltonian, the commutable one can be defined for the overlap fermion. The eigenvalues of the energy and the chiral charge can be defined simultaneously. We study how the eigenvalue spectrum reflects chiral properties of systems, such as a chiral chemical potential and the axial anomaly. We also show that the Wilson fermion is a chiral fermion in one dimension.

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$q$ deformed formulation of Hamiltonian SU(3) Yang-Mills theory

Tomoya Hayata, Yoshimasa Hidaka

2023年06月

　概要を見る

We study $\mathrm{SU}(3)$ Yang-Mills theory in $(2+1)$ dimensions based on
networks of Wilson lines. With the help of the $q$ deformation, networks
respect the (discretized) $\mathrm{SU}(3)$ gauge symmetry as a quantum group,
i.e., $\mathrm{SU}(3)_k$, and may enable implementations of $\mathrm{SU}(3)$
Yang-Mills theory in quantum and classical algorithms by referring to those of
the stringnet model. As a demonstration, we perform a mean-field computation of
the groundstate of $\mathrm{SU}(3)_k$ Yang-Mills theory, which is in good
agreement with the conventional Monte Carlo simulation by taking sufficiently
large $k$. The variational ansatz of the mean-field computation can be
represented by the tensor networks called infinite projected entangled pair
states. The success of the mean-field computation indicates that the essential
features of Yang-Mills theory are well described by tensor networks, so that
they may be useful in numerical simulations of Yang-Mills theory.


Non-Hermitian topological Fermi superfluid near the p-wave unitary limit

Tajima H., Sekino Y., Inotani D., Dohi A., Nagataki S., Hayata T.

Physical Review A （AMER PHYSICAL SOC）  107 （ 3 ）  2023年03月

査読有り,  ISSN  24699926

　概要を見る

We discuss theoretically the non-Hermitian superfluid phase transition in one-dimensional two-component Fermi gases near the p-wave Feshbach resonance accompanied by the two-body loss associated with dipolar relaxation. We point out that this system gives us an opportunity to explore the interplay among various nontrivial properties such as universal thermodynamics at divergent p-wave scattering lengths, the topological phase transition at vanishing chemical potential, and the non-Hermitian Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) transition, in a unified manner. In the BCS phase, the loss-induced superfluid-normal transition occurs when the exceptional point appears in the effective non-Hermitian Hamiltonian. In the BEC phase, the diffusive gapless mode can be regarded as a precursor of the instability of the superfluid state. Moreover, we show that the superfluid state is fragile against the two-body loss near the topological phase transition point.

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Dissipation-induced dynamical phase transition in postselected quantum trajectories

Hayata T., Hidaka Y., Yamamoto A.

Progress of Theoretical and Experimental Physics （OXFORD UNIV PRESS INC）  2023 （ 2 ）  2023年02月

査読有り,  ISSN  2050-3911

　概要を見る

It is known that effects of dissipation or measurement backreaction in postselected quantum trajectories are described by a non-Hermitian Hamiltonian, but their consequences in real-time dynamics of many-body systems are yet to be elucidated. Through a study of a non-Hermitian Hubbard model, we reveal a novel dissipation-induced dynamical phase transition in postselected quantum trajectories, where time controls the strength of postselection and becomes the intrinsic parameter inducing the phase transition. Our findings are testable in ultracold atom experiments and may open a new avenue in the dissipative engineering of quantum systems.

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Non-Hermitian topological Fermi superfluid near the -wave unitary limit

H Tajima, Y Sekino, D Inotani, A Dohi, S Nagataki, T Hayata

Physical Review A 107 (3), 033331 2023年

Lattice Lindblad simulation

Hayata T., Hidaka Y., Yamamoto A.

Progress of Theoretical and Experimental Physics （OXFORD UNIV PRESS INC）  2022 （ 5 ）  2022年05月

査読有り,  ISSN  2050-3911

　概要を見る

We perform real-Time lattice simulation of an open quantum system based on the Schwinger-Keldysh path integral representation of the Lindblad formalism. Although the real-Time simulation generally suffers from the sign problem, a few exceptional cases exist. We focus on a sign-problem-free system of a non-relativistic spinless fermion and analyze the time evolution under driving and dissipation.

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Diagnosis of information scrambling from Hamiltonian evolution under decoherence

Hayata T., Hidaka Y., Kikuchi Y.

Physical Review D （AMER PHYSICAL SOC）  104 （ 7 ）  2021年10月

査読有り,  ISSN  24700010

　概要を見る

We apply a quantum teleportation protocol based on the Hayden-Preskill thought experiment to quantify how scrambling a given quantum evolution is. It has an advantage over the direct measurement of out-of-time ordered correlators when used to diagnose the information scrambling in the presence of decoherence effects stemming from a noisy quantum device. We demonstrate the protocol by applying it to two physical systems: Ising spin chain and SU(2) lattice Yang-Mills theory. To this end, we numerically simulate the time evolution of the two theories in the Hamiltonian formalism. The lattice Yang-Mills theory is implemented with a suitable truncation of Hilbert space on the basis of the Kogut-Susskind formalism. On a two-leg ladder geometry and with the lowest nontrivial spin representations, it can be mapped to a spin chain, which we call the Yang-Mills-Ising model and is also directly applicable to future digital quantum simulations. We find that the Yang-Mills-Ising model shows the signal of information scrambling at late times.

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Non-Hermitian Hubbard model without the sign problem

Hayata T., Yamamoto A.

Physical Review B （AMER PHYSICAL SOC）  104 （ 12 ）  2021年09月

査読有り,  ISSN  24699950

　概要を見る

We study the Hubbard model with non-Hermitian asymmetric hopping terms. The conjugate hopping terms are introduced for two spin components so that the negative sign is canceled out. This ensures that the quantum Monte Carlo simulation is free from the negative sign problem. We analyze the antiferromagnetic order and its suppression by the non-Hermiticity.

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Thermalization of Yang-Mills theory in a (3+1)-dimensional small lattice system

Hayata T., Hidaka Y.

Physical Review D （AMER PHYSICAL SOC）  103 （ 9 ）  2021年05月

査読有り,  ISSN  24700010

　概要を見る

We study the real-time evolution of SU(2) Yang-Mills theory in a (3+1)-dimensional small lattice system after interaction quench. We numerically solve the Schrödinger equation with the Kogut-Susskind Hamiltonian in the physical Hilbert space obtained by solving Gauss law constraints. We observe the thermalization of a Wilson loop to the canonical state; the relaxation time is insensitive to the coupling strength and estimated as τeq∼2π/T with temperatures T at steady states. We also compute the vacuum persistence probability (the Loschmidt echo) to understand the relaxation from the dynamics of the wave function.

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Second order chiral kinetic theory under gravity and antiparallel charge-energy flow

Hayata T., Hidaka Y., Mameda K.

Journal of High Energy Physics （SPRINGER）  2021 （ 5 ）  2021年05月

査読有り,  ISSN  1029-8479

　概要を見る

We derive the chiral kinetic theory under the presence of a gravitational Riemann curvature. It is well-known that in the chiral kinetic theory there inevitably appears a redundant ambiguous vector corresponding to the choice of the Lorentz frame. We reveal that on top of this conventional frame choosing vector, higher-order quantum correction to the chiral kinetic theory brings an additional degrees of freedom to specify the distribution function. Based on this framework, we derive new types of fermionic transport, that is, the charge current and energy-momentum tensor induced by the gravitational Riemann curvature. Such novel phenomena arise not only under genuine gravity but also in a (pseudo-)relativistic fluid, for which inhomogeneous vorticity or temperature are effectively represented by spacetime metric tensor. It is especially found that the charge and energy currents are antiparallelly induced by an inhomogeneous fluid vorticity (more generally, by the Ricci tensor R0i), as a consequence of the spin-curvature coupling. We also briefly discuss possible applications to Weyl/Dirac semimetals and heavy-ion collision experiments.

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Thermalization of Yang-Mills theory in a ( )-dimensional small lattice system

T Hayata, Y Hidaka

Physical Review D 103 (9), 094502 2021年

Chiral vortical effect in relativistic and nonrelativistic systems

Atsuo Shitade, Kazuya Mameda, Tomoya Hayata

Physical Review B （American Physical Society (APS)）  102 （ 20 ）  2020年11月

査読有り,  ISSN  2469-9950

　概要を見る

We formulate the chiral vortical effect (CVE) and its generalization called generalized vortical effect using the semiclassical theory of wave packet dynamics. We take the spin-vorticity coupling into account and calculate the transport charge current by subtracting the magnetization one from the Noether local one. We find that the transport charge current in the CVE always vanishes in relativistic chiral fermions. This result implies that it cannot be observed in transport experiments in condensed matter systems such as Dirac/Weyl semimetals with the pseudo-Lorentz symmetry. We also demonstrate that the anisotropic CVE can be observed in nonrelativistic systems that belong to the point groups D-n, C-n (n = 2, 3, 4, 6), and C-1, such as n-type tellurium.

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String confinement in two-form lattice gauge theory

Tomoya Hayata, Arata Yamamoto

Physical Review D （AMER PHYSICAL SOC）  100 （ 7 ）  2019年10月

筆頭著者, 責任著者, 査読有り,  ISSN  2470-0010

　概要を見る

We study the confinement between vortex strings in the lattice gauge theory of the dual Abelian Higgs model. The dual lattice gauge theory is described by a two-form gauge field coupled with a one-form gauge field. We calculate the string-antistring potential from the surface operator of the two-form gauge field. The linear confining potential appears in the string confinement phase, and it disappears in the string deconfinement phase. The phase diagram of the theory is also obtained.

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Negative refractive index in cubic noncentrosymmetric superconductors

Hayata Tomoya

PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS （OXFORD UNIV PRESS INC）  2019 （ 3 ）  2019年03月

筆頭著者, 責任著者, 査読有り,  ISSN  2050-3911

　概要を見る

We study the negative refractive index in cubic noncentrosymmetric superconductors. We consider the Maxwell equations under the Meissner effect, and the magnetoelectric effect arising due to inversion-symmetry breaking. We derive the dispersion relations of electromagnetic waves and show that the refractive index becomes negative at frequencies just below the plasma gap. We find that the chiral mechanism of the negative refractive index, which is usually discussed in chiral materials with negative permittivity, can be directly applied to noncentrosymmetric superconductors with positive permittivity. A rough estimation from experimental values of the penetration depth of LiPt3B indicates that a negative refractive index may appear in UV regions.

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A new route to negative refractive index from topological metals

Hayata Tomoya

PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS （OXFORD UNIV PRESS INC）  2018 （ 8 ）  2018年08月

筆頭著者, 責任著者, 査読有り,  ISSN  2050-3911

　概要を見る

We discuss the possibility of realizing a negative refractive index in Weyl/Dirac semimetals. We consider the Maxwell equations with the plasma gap and chiral magnetic effect. By computing the dispersion relations of electromagnetic waves, we show that the refractive index becomes negative at frequencies (just) below the plasma frequency. We find that the axial anomaly, or, more specifically, the negative magnetoresistance (an electric current parallel to magnetic fields) opens a new route to realizing a negative refractive index. As an experimental implication, we compute the reflection and transmission coefficients of electromagnetic waves in a slab of Weyl/Dirac semimetals.

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Chiral magnetic effect of light

Tomoya Hayata

Physical Review B （American Physical Society）  97 （ 20 ）  2018年05月

筆頭著者, 責任著者, 査読有り,  ISSN  2469-9969

　概要を見る

We study a photonic analog of the chiral magnetic (vortical) effect. We discuss that the vector component of magnetoelectric tensors plays a role of "vector potential," and its rotation is understood as "magnetic field" of a light. Using the geometrical optics approximation, we show that "magnetic fields" cause an anomalous shift of a wave packet of a light through an interplay with the Berry curvature of photons. The mechanism is the same as that of the chiral magnetic (vortical) effect of a chiral fermion, so that we term the anomalous shift "chiral magnetic effect of a light." We further study the chiral magnetic effect of a light beyond geometric optics by directly solving the transmission problem of a wave packet at a surface of a magnetoelectric material. We show that the experimental signal of the chiral magnetic effect of a light is the nonvanishing of transverse displacements for the beam normally incident to a magnetoelectric material.

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Lattice simulation with the Majorana positivity

Arata Yamamoto, Tomoya Hayata

EPJ Web of Conferences （EDP Sciences）  175 2018年03月

査読有り,  ISSN  2100-014X

　概要を見る

While the sign problem of the Dirac fermion is conditioned by the semipositivity of a determinant, that of the Majorana fermion is conditioned by the semipositivity of a Pfaffian. We introduce one sufficient condition for the semi-positivity of a Pfaffian. Based on the semi-positivity condition, we study an effective model of the Majorana fermion. We also present the application to the Dirac fermion.

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Topological properties of the chiral magnetic effect in multi-Weyl semimetals

Tomoya Hayata, Yuta Kikuchi, Yuya Tanizaki

PHYSICAL REVIEW B （AMER PHYSICAL SOC）  96 （ 8 ）  2017年08月

査読有り,  ISSN  2469-9950

　概要を見る

We compute the chiral magnetic effect (CME) in multi-Weyl semimetals (multi-WSMs) based on the chiral kinetic theory. Multi-WSMs are WSMs with multiple monopole charges that have nonlinear and anisotropic dispersion relations near the Weyl points, and we need to extend the conventional computation of the CME in WSMs with linear dispersion relations. The topological properties of the CME in multi-WSMs are investigated in detail for not only static magnetic fields but also time-dependent (dynamic) ones. We propose an experimental setup to measure the multiple monopole charge via the topological nature hidden in the dynamic CME.

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Kinetic theory and anomalous transports in the presence of nonabelian phase-space Berry curvatures

Tomoya Hayata, Yoshimasa Hidaka

PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS （OXFORD UNIV PRESS INC）  2017 （ 7 ）  2017年07月

筆頭著者, 責任著者, 査読有り,  ISSN  2050-3911

　概要を見る

We study anomalous transport effects induced by the nonabelian Berry curvature. For that purpose we construct the kinetic theory in (2d)-dimensional phase space with abelian and nonabelian phase-space Berry curvatures. Then we calculate anomalous transport effects on the basis of the kinetic theory. As an example, we study anomalous charge and spin transport effects induced by the SU(2) Berry curvature such as the adiabatic spin pumping, the nonabelian chiral magnetic effect, and the spin analogue of the chiral magnetic effect. We also derive the topological effective theory to reproduce transport effects in insulators calculated from the kinetic theory. Such an effective theory is given by the nonabelian phase-space Chern-Simons theory.

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Quantum Monte Carlo simulation of a two-dimensional Majorana lattice model

Tomoya Hayata, Arata Yamamoto

PHYSICAL REVIEW B （AMER PHYSICAL SOC）  96 （ 3 ）  2017年07月

査読有り,  ISSN  2469-9950

　概要を見る

We study interacting Majorana fermions in two dimensions as a low-energy effective model of a vortex lattice in two-dimensional time-reversal-invariant topological superconductors. For that purpose, we implement ab initio quantum Monte Carlo simulation to the Majorana fermion system in which the path-integral measure is given by a semipositive Pfaffian. We discuss spontaneous breaking of time-reversal symmetry at finite temperatures.

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