論文 - 早田　智也

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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