論文 - 早田　智也

Phase transition on superfluid vortices in Higgs-Confinement crossover

Hayata T., Hidaka Y., Kondo D.

Journal of High Energy Physics 2025 （ 3 ）  2025年03月

　概要を見る

We propose a novel method to distinguish states of matter by identifying spontaneous symmetry breaking on extended objects, such as vortices, even in the absence of a bulk phase transition. As a specific example, we investigate the phase transition on superfluid vortices in the Higgs-confinement crossover using a U(1)gauge × U(1)global model in (3 + 1) dimensions. This model exhibits superfluidity of U(1)global symmetry and allows for a crossover between the Higgs and confinement regimes by varying the gauge coupling constant from weak to strong. We demonstrate that, on vortices, spontaneous breaking of the ℤ2 flavor symmetry occurs in the weak coupling (Higgs) regime, while it does not in the strong coupling (confinement) regime. We also confirm that those regimes are separated by a second-order phase transition through Monte Carlo simulations, whose universality class corresponds to the two-dimensional Ising model.

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Floquet evolution of the q-deformed SU(3)<inf>1</inf> Yang-Mills theory on a two-leg ladder

Hayata T., Hidaka Y.

Physical Review D 111 （ 3 ）  2025年02月

ISSN  24700010

　概要を見る

We simulate Floquet time evolution of a truncated SU(3) lattice Yang-Mills theory on a two-leg ladder geometry under open boundary conditions using IBM's superconducting 156-qubit device ibm_fez. To this end, we derive the quantum spin representation of the lattice Yang-Mills theory and compose a quantum circuit carefully tailored to hardware, reducing the number of controlled-Z gates. Since it is still challenging to simulate Hamiltonian evolution in present noisy quantum processors, we make the step size in the Suzuki-Trotter decomposition very large and simulate thermalization dynamics in Floquet circuit composed of the Suzuki-Trotter evolution. We demonstrate that IBM's Heron quantum processor can simulate, by error mitigation, Floquet thermalization dynamics in a large system consisting of 62 qubits. Our work would be a benchmark for further quantum simulations of lattice gauge theories using real devices.

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Floquet evolution of the -deformed Yang-Mills theory on a two-leg ladder

T Hayata, Y Hidaka

Physical Review D 111 (3), 034513 2025年

Floquet prethermalization of Z2 lattice gauge theory on superconducting qubits

Hayata T., Seki K., Yamamoto A.

Physical Review D 110 （ 11 ）  2024年12月

筆頭著者, 責任著者, 査読有り,  ISSN  24700010

　概要を見る

Simulating nonequilibirum dynamics of a quantum many-body system is one of the promising applications of quantum computing. We simulate the time evolution of one-dimensional Z2 lattice gauge theory on IBM's superconducting 156-qubit device, ibm_fez. We consider the Floquet circuit made of the Trotter decomposition of Hamiltonian evolution and focus on its dynamics toward thermalization. Quantum simulation with the help of error mitigation is successful in running the Floquet circuit made of 38 and 116 qubits up to 10 Trotter steps in the best case. This is enough to reach the early stage of prethermalization. Our work would be a benchmark for the potential power of quantum computing for high-energy physics problems.

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Chiral fermion on quantum computers

Yamamoto A., Hayata T., Nakayama K.

Proceedings of Science 453 2024年11月

ISSN  23318422

　概要を見る

Quantum computation often suffers from artificial symmetry breaking. We should strive to suppress the artifact both by theoretical and technological improvements. The theoretical formalism of the lattice fermion with exact chiral symmetry is called the chiral fermion. In this presentation, we show how the chiral fermion describes chiral physics in quantum computing. We also show that, although a drawback of the chiral fermion is large computational cost, there is a loophole in one dimension.

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Dense QCD<inf>2</inf> with matrix product states

Hayata T., Hidaka Y., Nishimura K.

Journal of High Energy Physics （Springer Science and Business Media LLC）  2024 （ 7 ）  2024年07月

査読有り,  ISSN  10298479

　概要を見る

We study one-flavor SU(2) and SU(3) lattice QCD in (1 + 1) dimensions at zero temperature and finite density using matrix product states and the density matrix renormalization group. We compute physical observables such as the equation of state, chiral condensate, and quark distribution function as functions of the baryon number density. As a physical implication, we discuss the inhomogeneous phase at nonzero baryon density, where the chiral condensate is inhomogeneous, and baryons form a crystal. We also discuss how the dynamical degrees of freedom change from hadrons to quarks through the formation of quark Fermi seas.

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Non-Hermitian p -wave superfluid and effects of the inelastic three-body loss in a one-dimensional spin-polarized Fermi gas

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

Physical Review Research 6 （ 2 ）  2024年04月

査読有り,  ISSN  26431564

　概要を見る

We theoretically investigate non-Hermitian p-wave Fermi superfluidity in one-dimensional spin-polarized Fermi gases which is relevant to recent ultracold atomic experiments. Considering an imaginary atom-dimer coupling responsible for the three-body recombination process in the Lindblad formalism, we discuss the stability of the superfluid state against the atomic loss effect. Within the two-channel non-Hermitian BCS-Eagles-Leggett theory, the atomic loss is characterized by the product of the imaginary atom-dimer coupling and the p-wave effective range. Our results indicate that for a given imaginary atom-dimer coupling, a smaller magnitude of the effective ranges of p-wave interaction is crucial for reaching the non-Hermitian p-wave Fermi superfluid state. Moreover, our theoretical framework for many-body systems with the three-body loss, which is inevitable in ultracold atoms, would promote further progress in non-Hermitian cold-atomic physics.

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Two-dimensional lattice with an imaginary magnetic field

Ozawa T., Hayata T.

Physical Review B （American Physical Society (APS)）  109 （ 8 ）  2024年02月

査読有り,  ISSN  24699950

　概要を見る

We introduce a two-dimensional non-Hermitian lattice model with an imaginary magnetic field and elucidate various unique features which are absent in Hermitian lattice models with real magnetic fields. To describe the imaginary magnetic field, we consider both the Landau gauge and the symmetric gauge, which are related by a generalized gauge transformation, changing not only the phase but also the amplitude of the wave function. We discuss the complex energy spectrum and the non-Hermitian Aharonov-Bohm effect as examples of properties which are due to the imaginary magnetic field independent of the generalized gauge transformation. We show that the energy spectrum does not converge as the lattice size is made larger, which comes from the intrinsic nonperiodicity of the model. However, we have found that the energy spectrum does converge if one fixes the length of one side and makes the other side longer; this asymptotic behavior can be understood in the framework of the non-Bloch band theory. We also find an analog of the Aharonov-Bohm effect; the net change of the norm of the wave function upon adiabatically forming a closed path is determined by the imaginary magnetic flux enclosed by the path, which provides an experimentally observable feature of the imaginary magnetic field.

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Dynamical chirality production in one dimension

Hayata T., Nakayama K., Yamamoto A.

Physical Review D 109 （ 3 ）  2024年02月

査読有り,  ISSN  24700010

　概要を見る

We discuss the quantum computation of dynamical chirality production in lattice gauge theory. Although the chirality of a lattice fermion is complicated in general dimensions, it can be simply formulated on a one-dimensional lattice. The chiral fermion formalism enables us to extract the physical part of the chirality production that would be interpreted as the chiral anomaly in the continuous theory. We demonstrate the computation of the Z2 lattice gauge theory on a classical emulator.

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Non-Hermitian -wave superfluid and effects of the inelastic three-body loss in a one-dimensional spin-polarized Fermi gas

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

Physical Review Research 6 (2), 023060 2024年

Floquet prethermalization of Z₂ lattice gauge theory on superconducting qubits

Hayata, T. and Seki, K. and Yamamoto, A.

arXiv 2024年

ISSN  23318422

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Floquet prethermalization of lattice gauge theory on superconducting qubits

T Hayata, K Seki, A Yamamoto

Physical Review D 110 (11), 114503 2024年

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

Hayata T., Hidaka Y.

Journal of High Energy Physics 2023 （ 9 ）  2023年09月

査読有り,  ISSN  1029-8479

　概要を見る

We study 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) SU(3) gauge symmetry as a quantum group, i.e., SU(3) k, and may enable implementations of 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 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.

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String-net formulation of Hamiltonian lattice Yang-Mills theories and quantum many-body scars in a nonabelian gauge theory

Hayata T., Hidaka Y.

Journal of High Energy Physics 2023 （ 9 ）  2023年09月

査読有り,  ISSN  1029-8479

　概要を見る

We study the Hamiltonian lattice Yang-Mills theory based on spin networks that provide a useful basis to represent the physical states satisfying the Gauss law constraints. We focus on SU(2) Yang-Mills theory in (2 + 1) dimensions. Following the string-net model, we introduce a regularization of the Kogut-Susskind Hamiltonian of lattice Yang-Mills theory based on the q deformation, which respects the (discretized) SU(2) gauge symmetry as quantum group, i.e., SU(2)k, and enables implementation of the lattice Yang-Mills theory both in classical and quantum algorithms by referring to those of the string-net model. Using the regularized Hamiltonian, we study quantum scars in a nonabelian gauge theory. Quantum scars are nonthermal energy eigenstates arising in the constrained quantum many-body systems. We find that quantum scars from zero modes, which have been found in abelian gauge theories arise even in a nonabelian gauge theory. We also show the spectrum of a single-plaquette model for SU(2)k and SU(3)k with naive cutoff and that based on the q-deformation to discuss cutoff dependence of the formulation.

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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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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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Momentum-space electromagnetic induction in Weyl semimetals

Hiroaki Ishizuka, Tomoya Hayata, Masahito Ueda, Naoto Nagaosa

PHYSICAL REVIEW B （AMER PHYSICAL SOC）  95 （ 24 ）  2017年06月

査読有り,  ISSN  2469-9950

　概要を見る

We theoretically study the effect of the Berry curvature on the transport properties of Weyl semimetals using a semiclassical Boltzmann transport theory, which results in nonlinear optical responses. In the adiabatic process, the Berry curvature, which involves the time derivative of the Bloch states, contributes to the transport properties such as the adiabatic Thouless pump. Although this effect is very weak in usual solids, it is enhanced in Weyl semimetals, where the Berry curvature contributes to observable nonlinear optical responses due to its nodal structure. In this paper, using the semiclassical Boltzmann theory, we show that a dc photocurrent induced by the Berry curvature robustly persists even in the limit of short scattering time. We also show that the photocurrent is well explained as a consequence of the electromagnetic induction in momentum space. The results indicate that the electromagnetic induction gives rise to a nondissipative photocurrent that is robust against decoherence within a time scale shorter than the periodicity of the incident electromagnetic field. We also discuss the second harmonic response of an ac current when the electron distribution is displaced from the ground state by an external field.

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Classification of sign-problem-free relativistic fermions on the basis of the Majorana positivity

Tomoya Hayata, Arata Yamamoto

PROGRESS OF THEORETICAL AND EXPERIMENTAL PHYSICS （OXFORD UNIV PRESS INC）  2017 （ 4 ）  2017年04月

筆頭著者, 責任著者, 査読有り,  ISSN  2050-3911

　概要を見る

We classify the sign-problem-free relativistic fermion actions on the basis of the Majorana representation. In the Majorana representation, the sign-problem-free condition is given by the semi-positivity of a Pfaffian. We show that the known sign-problem-free actions of the Dirac fermions, which are usually understood from the semi-positivity of a determinant, e.g., the action of quantum chromodynamics with nonzero chiral chemical potential or nonzero isospin chemical potential, can also be understood from the semi-positivity of a Pfaffian. We also derive new classes of the sign-problem-free relativistic fermion actions with Majorana-type source terms.

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Kinetic derivation of generalized phase space Chern-Simons theory

Tomoya Hayata, Yoshimasa Hidaka

PHYSICAL REVIEW B （AMER PHYSICAL SOC）  95 （ 12 ）  2017年03月

筆頭著者, 責任著者, 査読有り,  ISSN  2469-9950

　概要を見る

We study anomalous transport phenomena induced by phase space Berry curvature. For that purpose we construct a kinetic theory in 2d phase space when all Abelian Berry curvatures are nonzero. We derive anomalous currents by calculating the complete form of the Poisson brackets of phase space coordinates. Then we construct the low-energy effective theory to reproduce the anomalous currents obtained from the kinetic theory. Such an effective theory is given by the Chern-Simons theory in 1 + 2d dimensions. Some implications of the Chern-Simons theory are also discussed.

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Emergent Electromagnetic Induction and Adiabatic Charge Pumping in Noncentrosymmetric Weyl Semimetals

Hiroaki Ishizuka, Tomoya Hayata, Masahito Ueda, Naoto Nagaosa

PHYSICAL REVIEW LETTERS （AMER PHYSICAL SOC）  117 （ 21 ）  2016年11月

査読有り,  ISSN  0031-9007

　概要を見る

The photovoltaic effect due to the adiabatic quantum phase in noncentrosymmetric Weyl semimetals is studied. We particularly focus on the case in which an external ac electric field is applied. By considering a generalized Weyl Hamiltonian with nonlinear terms, we show that the photocurrent is induced by circularly, rather than linearly, polarized light. This photovoltaic current can be understood as an emergent electromagnetic induction in momentum space; the Weyl node is a magnetic monopole in momentum space, the circular motion of which induces the electric field. This result is distinct from conventional photovoltaic effects, and the estimated photocurrent is similar to 10(-1)-10(1) nA, which can be detected experimentally.

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Complex saddle points and the sign problem in complex Langevin simulation

Tomoya Hayata, Yoshimasa Hidaka, Yuya Tanizaki

NUCLEAR PHYSICS B （ELSEVIER SCIENCE BV）  911   94 - 105 2016年10月

筆頭著者, 責任著者, 査読有り,  ISSN  0550-3213

　概要を見る

We show that complex Langevin simulation converges to a wrong result within the semiclassical analysis, by relating it to the Lefschetz-thimble path integral, when the path-integral weight has different phases among dominant complex saddle points. Equilibrium solution of the complex Langevin equation forms local distributions around complex saddle points. Its ensemble average approximately becomes a direct sum of the average in each local distribution, where relative phases among them are dropped. We propose that by taking these phases into account through reweighting, we can solve the wrong convergence problem. However, this prescription may lead to a recurrence of the sign problem in the complex Langevin method for quantum many-body systems. (C) 2016 The Author(s). Published by Elsevier B.V.

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Lefschetz-thimble analysis of the sign problem in one-site fermion model

Yuya Tanizaki, Yoshimasa Hidaka, Tomoya Hayata

NEW JOURNAL OF PHYSICS （IOP PUBLISHING LTD）  18 （ 3 ）  2016年03月

査読有り,  ISSN  1367-2630

　概要を見る

The Lefschetz-thimble approach to path integrals is applied to a one-site model of electrons, i.e., the one-site Hubbard model. Since the one-site Hubbard model shows a non-analytic behavior at the zero temperature and its path integral expression has the sign problem, this toy model is a good testing ground for an idea or a technique to attack the sign problem. Semiclassical analysis using complex saddle points unveils the significance of interference among multiple Lefschetz thimbles to reproduce the non-analytic behavior by using the path integral. If the number of Lefschetz thimbles is insufficient, we found not only large discrepancies from the exact result, but also thermodynamic instabilities. Analyzing such singular behaviors semiclassically, we propose a criterion to identify the necessary number of Lefschetz thimbles. We argue that this interference of multiple saddle points is a key issue to understand the sign problem of the finite-density quantum chromodynamics.

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Lefschetz-thimble approach to the Silver Blaze problem of one-site fermion model

Tanizaki Y, Hidaka Y, Hayata T

Proceedings of Science Part F128557 2016年

査読有り

　概要を見る

The sign problem of finite-density QCD at the zero temperature becomes very
severe if the quark chemical potential exceeds half of the pion mass. In order
to understand its property, we consider the sign problem of the one-site
fermion model appearing in its path-integral expression by using the
Lefschetz-thimble method. We show that the original integration cycle becomes
decomposed into multiple Lefschetz thimbles at a certain value of the fermion
chemical potential, which would correspond to half of the pion mass of
finite-density QCD. This triggers a fictitious phase transition on each
Lefschetz thimble, and the interference of complex phases among them plays an
important role for the correct description of the system. We also show that the
complex Langevin method does not work in this situation.

Complex Langevin simulation of quantum vortices in a Bose-Einstein condensate

Tomoya Hayata, Arata Yamamoto

Physical Review A - Atomic, Molecular, and Optical Physics （American Physical Society）  92 （ 4 ）  2015年10月

筆頭著者, 責任著者, 査読有り,  ISSN  1094-1622

　概要を見る

The ab initio simulation of quantum vortices in a Bose-Einstein condensate is performed by adopting the complex Langevin techniques. We simulate the nonrelativistic boson field theory at finite chemical potential under rotation. In the superfluid phase, vortices are generated above a critical angular velocity and the circulation is clearly quantized even in the presence of quantum fluctuations.

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Relativistic hydrodynamics from quantum field theory on the basis of the generalized Gibbs ensemble method

Tomoya Hayata, Yoshimasa Hidaka, Toshifumi Noumi, Masaru Hongo

Physical Review D - Particles, Fields, Gravitation and Cosmology （American Physical Society）  92 （ 6 ）  2015年09月

査読有り,  ISSN  1550-2368

　概要を見る

We derive relativistic hydrodynamics from quantum field theories by assuming that the density operator is given by a local Gibbs distribution at initial time. We decompose the energy-momentum tensor and particle current into nondissipative and dissipative parts, and analyze their time evolution in detail. Performing the path-integral formulation of the local Gibbs distribution, we microscopically derive the generating functional for the nondissipative hydrodynamics. We also construct a basis to study dissipative corrections. In particular, we derive the first-order dissipative hydrodynamic equations without a choice of frame such as the Landau-Lifshitz or Eckart frame.

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Inhomogeneous Polyakov loop induced by inhomogeneous chiral condensates

Tomoya Hayata, Arata Yamamoto

PHYSICS LETTERS B （ELSEVIER SCIENCE BV）  744   401 - 405 2015年05月

筆頭著者, 責任著者, 査読有り,  ISSN  0370-2693

　概要を見る

We study the spatial inhomogeneity of the Polyakov loop induced by inhomogeneous chiral condensates. We formulate an effective model of gluons on the background fields of chiral condensates, and perform its lattice simulation. On the background of inhomogeneous chiral condensates, the Polyakov loop exhibits an in-phase spatial oscillation with the chiral condensates. We also analyze the heavy quark potential and show that the inhomogeneous Polyakov loop indicates the inhomogeneous confinement of heavy quarks. (C) 2015 The Authors. Published by Elsevier B.V.

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Dispersion relations of Nambu-Goldstone modes at finite temperature and density

Tomoya Hayata, Yoshimasa Hidaka

Physical Review D - Particles, Fields, Gravitation and Cosmology （American Physical Society）  91 （ 5 ）  2015年03月

査読有り,  ISSN  1550-2368

　概要を見る

We discuss the dispersion relations of Nambu-Goldstone (NG) modes associated with spontaneous breaking of internal symmetries at finite temperature and/or density. We show that the dispersion relations of type-A (I) and type-B (II) NG modes are linear and quadratic in momentum, whose imaginary parts are quadratic and quartic, respectively. In both cases, the real parts of the dispersion relations are larger than the imaginary parts when the momentum is small, so that the NG modes can propagate far away. We derive the gap formula for NG modes in the presence of a small explicit breaking term. We also discuss the gapped partners of type-B NG modes, when the expectation values of a charge density and a local operator that break the same symmetry coexist.

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Complex langevin simulation in condensed matter physics

Yamamoto A, Hayata T

Proceedings of Science 14-18-July-2015 2015年

査読有り

　概要を見る

The complex Langevin method is one hopeful candidate to tackle the sign
problem. This method is applicable not only to QCD but also to nonrelativistic
field theory, such as condensed matter physics. We present the simulation
results of a rotating Bose gas and an imbalanced Fermi-Hubbard model.

Broken spacetime symmetries and elastic variables

Tomoya Hayata, Yoshimasa Hidaka

PHYSICS LETTERS B （ELSEVIER SCIENCE BV）  735   195 - 199 2014年07月

査読有り,  ISSN  0370-2693

　概要を見る

We discuss spontaneous breaking of continuum symmetries, whose generators do explicitly depend on the spacetime coordinates. We clarify the relation between broken symmetries and elastic variables at both zero and finite temperatures, and/or finite densities, and show the general counting rule that is model-independently determined by the symmetry breaking pattern. We apply it to three intriguing examples: rotational, conformal, and gauge symmetries. (C) 2014 The Authors. Published by Elsevier B. V.

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Schwinger mechanism with stochastic quantization

Kenji Fukushima, Tomoya Hayata

PHYSICS LETTERS B （ELSEVIER SCIENCE BV）  735   371 - 375 2014年07月

査読有り,  ISSN  0370-2693

　概要を見る

We prescribe a formulation of the particle production with real-time Stochastic Quantization. To construct the retarded and the time-ordered propagators we decompose the stochastic variables into positive- and negative-energy parts. In this way we demonstrate how to derive a standard formula for the Schwinger mechanism under time-dependent electric fields. We discuss a mapping to the Schwinger-Keldysh formalism and a relation to the classical statistical simulation. (C) 2014 The Authors. Published by Elsevier B.V.

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Temporal chiral spiral in QCD in the presence of strong magnetic fields

Tomoya Hayata, Yoshimasa Hidaka, Arata Yamamoto

PHYSICAL REVIEW D （AMER PHYSICAL SOC）  89 （ 8 ）  2014年04月

筆頭著者, 責任著者, 査読有り,  ISSN  1550-7998

　概要を見る

Vacuum properties of quantum chromodynamics in strong magnetic and finite electric fields are investigated. We show that when a uniform electric field is instantaneously applied in the parallel direction to a strong magnetic field, it induces temporal oscillation of the scalar and pseudoscalar condensates. This is a temporal analog to the chiral spiral. The oscillation originates with the propagation of the collective mode, which is protected by the axial anomaly and thus is nondissipative.

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Sign problem and the chiral spiral on the finite density lattice

Ryutaro Fukuda, Kenji Fukushima, Tomoya Hayata, Yoshimasa Hidaka

PHYSICAL REVIEW D （AMER PHYSICAL SOC）  89 （ 1 ）  2014年01月

査読有り,  ISSN  1550-7998

　概要を見る

We investigate the sign problem of the fermion determinant at finite baryon density in (1 + 1) dimensions, in which the ground state in the chiral limit should be free from the sign problem by forming a chiral spiral. To confirm it, we evaluate the fermion determinant in the continuum theory at the one-loop level and find that the determinant becomes real as expected. The conventional lattice formulation to implement a chemical potential is, however, not compatible with the spiral transformation. We discuss an alternative of the finite-density formulation and numerically verify the chiral spiral on the finite density lattice.

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Dynamical mass generation of vector mesons from QCD trace anomaly

Tomoya Hayata

PHYSICAL REVIEW D （AMER PHYSICAL SOC）  88 （ 3 ）  2013年08月

筆頭著者, 責任著者, 査読有り,  ISSN  1550-7998

　概要を見る

Mass formulas for the vector mesons written in terms of the gluon condensate, i.e., the trace anomaly in quantum chromodynamics (QCD), are derived on the basis of finite energy QCD sum rules. We utilize sum rules with s(n) and s(n+1/2) weights, which relate the energy-weighted spectral sums to the vacuum expectation values of certain commutation relations. After evaluating the commutation relations, the sum rules with s(n) weights are reduced to the familiar ones obtained from the operator product expansion (OPE). On the other hand, the sum rules with s(n+1/2) weights cannot be derived from OPE. They give new relations between the spectral sums and QCD vacuum fluctuations. To derive a simple mass formula, we adopt the pole + continuum ansatz for the spectral function, and we solve coupled equations given by the sum rules with s(0,1) weights and the new sum rule with s(1/2) weight. Application of our approach to the axial-vector meson is also discussed.

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Time-dependent heavy-quark potential at finite temperature from gauge-gravity duality

Tomoya Hayata, Kanabu Nawa, Tetsuo Hatsuda

Physical Review D - Particles, Fields, Gravitation and Cosmology （American Physical Society (APS)）  87 （ 10 ）  2013年05月

筆頭著者, 責任著者, 査読有り,  ISSN  1550-7998

　概要を見る

The potential between a heavy quark and an antiquark inside the quark-gluon plasma is studied on the basis of the gauge-gravity duality. A real-time complex potential VQQ̄(t,r) is derived from the Wilson loop, which is evaluated by its gravity dual in the Euclidean five-dimensional anti-de Sitter black hole metric. To make the analytic continuation from the imaginary time to the real time, specific variational configurations of the string world sheet in the Euclidean metric are introduced. A rapid approach of V QQ̄(t,r) to its stationary value is found at the time scale t (πT)-1, and the imaginary part of VQQ̄(r) becomes significant above the length scale r=1.72(πT)-1. Also, these scales are independent of the 't Hooft coupling λ. Implications of these results to the properties of heavy quarkonia in quark-gluon plasma are briefly discussed. © 2013 American Physical Society.

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New QCD sum rules based on canonical commutation relations

Tomoya Hayata

PROGRESS IN PARTICLE AND NUCLEAR PHYSICS （ELSEVIER SCIENCE BV）  67 （ 2 ） 136 - 139 2012年04月

筆頭著者, 責任著者, 査読有り,  ISSN  0146-6410

　概要を見る

New derivation of QCD sum rules by canonical commutators is developed. It is the simple and straightforward generalization of Thomas-Reiche-Kuhn sum rule on the basis of Kugo-Ojima operator formalism of a non-abelian gauge theory and a suitable subtraction of UV divergences. By applying the method to the vector and axial vector current in QCD, the exact Weinberg's sum rules are examined. Vector current sum rules and new fractional power sum rules are also discussed. (C) 2011 Elsevier B.V. All rights reserved.

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Resealed Perturbation Theory

Tomoya Hayata

PROGRESS OF THEORETICAL PHYSICS （PROGRESS THEORETICAL PHYSICS PUBLICATION OFFICE）  124 （ 6 ） 1097 - 1104 2010年12月

筆頭著者, 責任著者, 査読有り,  ISSN  0033-068X

　概要を見る

A nonperturbative method that can go beyond the weak coupling perturbation theory is introduced. The essential idea is to formulate a set of exact differential equations as a function of coupling strength g. Unlike other resummation methods in which information on higher-order terms is necessary, we only need a leading-order perturbative formula in every step to reach a large value of g. The method is applied to the quantum anharmonic oscillator and quantum double-well potential in one dimension. Both are known to have divergent series in the weak coupling perturbation and the latter is not Borel-summable. Our method is shown to work well from the weak coupling to the strong coupling for the energy eigenvalues and the wave functions. The method is also applied successfully to a system with a time-dependent external field.

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