arXiv subjects

Masaru Hongo

Publications and source records attributed to Masaru Hongo.

36 records · Page 2Linked to original sources

arXiv2021

Analytical WKB theory for high-harmonic generation and its application to massive Dirac electrons

We propose an analytical approach to high-harmonic generation (HHG) for nonperturbative low-frequency and high-intensity fields based on the (Jeffreys-)Wentzel-Kramers-Brillouin (WKB) approximation. By properly taking into account Stokes phenomena of WKB solutions, we obtain wavefunctions that systematically include the repetitive dynamics of production and acceleration of electron-hole pairs and quantum interference due to phase accumulation between different pair production times (Stückelberg phase). Using the obtained wavefunctions without relying on any phenomenological assumptions, we explicitly compute electric current (including intra- and inter-band contributions) as the source of HHG for a massive Dirac system in (1+1)-dimensions under an ac electric field. We demonstrate that the WKB approximation agrees well with numerical results obtained by solving the time-dependent Schrödinger equation and point out that the quantum interference is important in HHG. We also predict in the deep nonperturbative regime that (1) harmonic intensities oscillate with respect to electric-field amplitude $E_0$ and frequency $Ω$, with a period determined by the Stückelberg phase; (2) the cutoff order of HHG is determined by $2eE_0/\hbar Ω^2$, with $e$ being the electron charge; and that (3) non-integer harmonics, controlled by the Stückelberg phase, appear as a transient effect. Our WKB theory is particularly suited for a parameter regime, where the Keldysh parameter $γ=(Δ/2)Ω/eE_0$, with $Δ$ being the gap size, is small. This parameter regime corresponds to intense lasers in the terahertz regime for realistic massive Dirac materials. Our analysis implies that the so-called HHG plateau can be observed at the terahertz frequency within the current technology.

cond-mat.str-el↗

arXiv2021

Anomaly-induced edge currents in hydrodynamics with parity anomaly

In this paper, we discuss relativistic hydrodynamics for a massless Dirac fermion in $(2+1)$ dimensions, which has the parity anomaly -- a global 't Hooft anomaly between $\mathrm{U}(1)$ and parity symmetries. We investigate how hydrodynamics implements the party anomaly, particularly focusing on the transport phenomena at the boundary. Based on the parity anomaly matching and the second law of local thermodynamics, we find $\mathrm{U}(1)$ and entropy currents localized at the boundary as well as the bulk anomalous current with vanishing divergence. These edge currents are similar to the $(1+1)$-dimensional chiral transports, but the coefficients are given by half of theirs. We also generalize our discussion to more general anomalies among multiple $\mathrm{U}(1)$ symmetries and single $\mathbb{Z}_2$ symmetry.

hep-th↗

arXiv2021

Quantum hydrodynamics from local thermal pure states

We provide a pure state formulation for hydrodynamic dynamics of isolated quantum many-body systems. A pure state describing quantum systems in local thermal equilibrium is constructed, which we call a local thermal pure quantum ($\ell$TPQ) state. We show that the thermodynamic functional and the expectation values of local operators (including a real-time correlation function) calculated from the $\ell$TPQ state converge to those from a local Gibbs ensemble in the large fluid-cell limit. As a numerical demonstration, we investigate a one-dimensional spin chain and observe the hydrodynamic relaxation obeying the Fourier's law. We further prove the second law of thermodynamics and the quantum fluctuation theorem, which are also validated numerically. The $\ell$TPQ formulation gives a useful theoretical basis to describe the emergent hydrodynamic behavior of quantum many-body systems furnished with a numerical efficiency, being applicable to both the non-relativistic and relativistic regimes.

cond-mat.stat-mech↗

arXiv2021

Microscopic theory of the fluctuating hydrodynamics in nonlinear lattices

The theory of fluctuating hydrodynamics has been an important tool for analyzing macroscopic behavior in nonlinear lattices. However, despite its practical success, its microscopic derivation is still incomplete. In this work, we provide the microscopic derivation of fluctuating hydrodynamics, using the coarse-graining and projection technique; the equivalence of ensembles turns out to be critical. The Green-Kubo (GK) like formula for the bare transport coefficients is presented in a numerically computable form. Our numerical simulations show that the bare transport coefficients exist for a sufficiently large but finite coarse-graining length in the infinite lattice within the framework of the GK like formula. This demonstrates that the bare transport coefficients uniquely exist for each physical system.

cond-mat.stat-mech↗

arXiv2020

Effective field theory of magnon: Dynamics in chiral magnets and Schwinger mechanism

We develop the effective field theoretical descriptions of spin systems in the presence of symmetry-breaking effects: the magnetic field, single-ion anisotropy, and Dzyaloshinskii-Moriya interaction. Starting from the lattice description of spin systems, we show that the symmetry-breaking terms corresponding to the above effects can be incorporated into the effective field theory as a combination of a background (or spurious) $\SO(3)$ gauge field and a scalar field in the symmetric tensor representation, which are eventually fixed at their physical values. We use the effective field theory to investigate mode spectra of inhomogeneous ground states, with focusing on one-dimensionally inhomogeneous states, such as helical and spiral states. Although the helical and spiral ground states share a common feature of supporting the gapless Nambu-Goldstone modes associated with the translational symmetry breaking, they have qualitatively different dispersion relations: isotropic in the helical phase while anisotropic in the spiral phase. We also discuss the magnon production induced by an inhomogeneous magnetic field, and find a formula akin to the Schwinger formula. Our formula for the magnon production gives a finite rate for antiferromagnets, and a vanishing rate for ferromagnets, whereas that for ferrimagnets interpolates between the two cases.

cond-mat.mes-hall↗

arXiv2020

Global anomaly matching in higher-dimensional $\mathbb{CP}^{N-1}$ model

We investigate 't Hooft anomalies in the $\mathbb{CP}^{N-1}$ model in spacetime dimensions higher than two and identify two types of anomalies: One is a mixed anomaly between the $\mathrm{PSU}(N)$ flavor-rotation and magnetic symmetries, and the other is between the reflection and magnetic symmetries. The latter indicates that even in the absence of the flavor symmetry, the model cannot have a unique gapped ground state as long as the reflection and magnetic symmetries are respected. We also clarified the condition for the 't Hooft anomalies to survive under monopole deformations, which explicitly break the magnetic symmetry down to its discrete subgroup. Besides, we explicitly show how the identified 't Hooft anomalies match in the low-energy effective description of symmetry broken phases---the Néel, $\mathrm{U}(1)$ spin liquid, and the valence bond solid phases. An application to the finite-temperature phase diagram of the four-dimensional $\mathbb{CP}^{N-1}$ model is also discussed.

cond-mat.str-el↗

arXiv2019

Effective Lagrangian for Nambu-Goldstone modes in nonequilibrium open systems

We develop the effective field theory of diffusive Nambu-Goldstone (NG) modes associated with spontaneous internal symmetry breaking taking place in nonequilibrium open systems. The effective Lagrangian describing semi-classical dynamics of the NG modes is derived and matching conditions for low-energy coefficients are also investigated. Due to new terms peculiar to open systems, the associated NG modes show diffusive gapless behaviors in contrast to the propagating NG mode in closed systems. We demonstrate two typical situations relevant to the condensed matter physics and high-energy physics, where diffusive type-A or type-B NG modes appear.

hep-th↗

arXiv2019

Instantons in Chiral Magnets

We exhaustively construct instanton solutions and elucidate their properties in one-dimensional anti-ferromagnetic chiral magnets based on the $O(3)$ nonlinear sigma model description of spin chains with the Dzyaloshinskii-Moriya (DM) interaction. By introducing an easy-axis potential and a staggered magnetic field, we obtain a phase diagram consisting of ground-state phases with two points (or one point) in the easy-axis dominant cases, a helical modulation at a fixed latitude of the sphere, and a tricritical point allowing helical modulations at an arbitrary latitude. We find that instantons (or skyrmions in two-dimensional Euclidean space) appear as composite solitons in different fashions in these phases: temporal domain walls or wall-antiwall pairs (bions) in the easy-axis dominant cases, dislocations (or phase slips) with fractional instanton numbers in the helical state, and isolated instantons and calorons living on the top of the helical modulation at the tricritical point. We also show that the models with DM interaction and an easy-plane potential can be mapped into those without them, providing a useful tool to investigate the model with the DM interaction.

cond-mat.mes-hall↗

arXiv2019

Fate of spin polarization in a relativistic fluid: An entropy-current analysis

We derive relativistic hydrodynamic equations with a dynamical spin degree of freedom on the basis of an entropy-current analysis. The first and second laws of local thermodynamics constrain possible structures of the constitutive relations including a spin current and the antisymmetric part of the (canonical) energy-momentum tensor. Solving the obtained hydrodynamic equations within the linear-mode analysis, we find spin-diffusion modes, indicating that spin density is damped out after a characteristic time scale controlled by transport coefficients introduced in the antisymmetric part of the energy-momentum tensor in the entropy-current analysis. This is a consequence of mutual convertibility between spin and orbital angular momentum.

hep-th↗

arXiv2019

Anomaly-induced transport phenomena from the imaginary-time formalism

A derivation of the anomaly-induced transport phenomena---the chiral magnetic/vortical effect---is revisited based on the imaginary-time formalism of quantum field theory. Considering the simplest anomalous system composed of a single Weyl fermion, we provide two derivations: perturbative (one-loop) evaluation of the anomalous transport coefficient, and the anomaly matching for the local thermodynamic functional.

hep-th↗

arXiv2019

Phase structure of the twisted $SU(3)/U(1)^2$ flag sigma model on $\mathbb{R}\times S^1$

We investigate the phase structure of the compactified $2$-dimensional nonlinear $SU(3)/U(1)^2$ flag sigma model with respect to two $θ$-terms. Based on the circle compactification with the ${\mathbb Z}_{3}$-twisted boundary condition, which preserves an 't Hooft anomaly of the original uncompactified theory, we perform the semiclassical analysis based on the dilute instanton gas approximation (DIGA). We clarify classical vacua of the theory and derive fractional instanton solutions connecting these vacua. The resulting phase structure based on DIGA exhibits the quantum phase transitions and triple degeneracy at special points in the $(θ_1,θ_2)$-plane, which is consistent with the phase diagram obtained from the anomaly matching and global inconsistency conditions. This result indicates the adiabatic continuity between the flag sigma models on ${\mathbb R}^{2}$ and ${\mathbb R}\times S^{1}$ with small compactification radius. We further estimate contributions from instanton--anti-instanton configuration (bion) and show the existence of the imaginary ambiguity, which is expected to be cancelled by that of the perturbative Borel resummation.

hep-th↗

arXiv2018

Does the chiral magnetic effect change the dynamic universality class in QCD?

In QCD matter under an external magnetic field, the chiral magnetic effect (CME) leads to the collective gapless mode called the chiral magnetic wave (CMW). Since dynamic universality class generally depends on low-energy gapless modes, it is nontrivial whether the CME and the resulting CMW change that of the second-order chiral phase transition in QCD. To address this question, we study the critical dynamics near the chiral phase transition in massless two-flavor QCD under an external magnetic field. By performing the dynamic renormalization-group analysis within the epsilon expansion, we find that the presence of the CME changes the dynamic universality class to that of model A. We also show that the transport coefficient of the CME is not renormalized by the critical fluctuations of the order parameter.

hep-ph↗

arXiv2018

Effective field theory of time-translational symmetry breaking in nonequilibrium open system

We develop the effective field theoretical (EFT) approach to time-translational symmetry breaking of nonequilibrium open systems based on the Schwinger-Keldysh formalism. In the Schwinger-Keldysh formalism, all the symmetries of the microscopic Lagrangian are doubled essentially because the dynamical fields are doubled to describe the time-evolution along the closed-time-path. The effective Lagrangian for open systems are then obtained by coarse-graining the microscopic Schwinger-Keldysh Lagrangian. As a consequence of coarse-graining procedure, there appear the noise and dissipation effects, which explicitly break the doubled time-translational symmetries into a diagonal one. We therefore need to incorporate this symmetry structure to construct the EFT for Nambu-Goldstone bosons in symmetry broken phases of open systems. Based on this observation together with the consistency of the Schwinger-Keldysh action, we construct and study the general EFT for time-translational symmetry breaking in particular, having in mind applications to synchronization, time crystal, and cosmic inflation.

hep-th↗

arXiv2018

Nonrelativistic hydrodynamics from quantum field theory: (I) Normal fluid composed of spinless Schrödinger fields

We provide a complete derivation of hydrodynamic equations for nonrelativistic systems based on quantum field theories of spinless Schrödeinger fields, assuming that an initial density operator takes a special form of the local Gibbs distribution. The constructed optimized/renormalized perturbation theory for real-time evolution enables us to separately evaluate dissipative and nondissipative parts of constitutive relations. It is shown that the path-integral formula for local thermal equilibrium together with the symmetry properties of the resulting action---the nonrelativistic diffeomorphism and gauge symmetry in the thermally emergent Newton-Cartan geometry---provides a systematic way to derive the nondissipative part of constitutive relations. We further show that dissipative parts are accompanied with the entropy production operator together with two kinds of fluctuation theorems by the use of which we derive the dissipative part of constitutive relations and the second law of thermodynamics. After obtaining the exact expression for constitutive relations, we perform the derivative expansion and derive the first-order hydrodynamic (Navier-Stokes) equation with the Green-Kubo formula for transport coefficients.

cond-mat.stat-mech↗

arXiv2017

Anomalous-hydrodynamic analysis of charge-dependent elliptic flow in heavy-ion collisions

Anomalous hydrodynamics is a low-energy effective theory that captures effects of quantum anomalies. We develop a numerical code of anomalous hydrodynamics and apply it to dynamics of heavy-ion collisions, where anomalous transports are expected to occur. This is the first attempt to perform fully non-linear numerical simulations of anomalous hydrodynamics. We discuss implications of the simulations for possible experimental observations of anomalous transport effects. From analyses of the charge-dependent elliptic flow parameters ($v_2^\pm$) as a function of the net charge asymmetry $A_\pm$, we find that the linear dependence of $Δv_2^\pm \equiv v_2^- - v_2^+$ on the net charge asymmetry $A_\pm$ cannot be regarded as a robust signal of anomalous transports, contrary to previous studies. We, however, find that the intercept $Δv_2^\pm(A_\pm=0)$ is sensitive to anomalous transport effects.

nucl-th↗

arXiv2016

Path-integral formula for local thermal equilibrium

We develop a complete path-integral formulation of relativistic quantum fields in local thermal equilibrium, which brings about the emergence of thermally induced curved spacetime. The resulting action is shown to have full diffeomorphism invariance and gauge invariance in thermal spacetime with imaginary-time independent backgrounds. This leads to the notable symmetry properties of emergent thermal spacetime: Kaluza-Klein gauge symmetry, spatial diffeomorphism symmetry, and gauge symmetry. A thermodynamic potential in local thermal equilibrium, or the so-called Masseiu-Planck functional, is identified as a generating functional for conserved currents such as the energy-momentum tensor and the electric current.

hep-th↗

arXiv2015

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

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.

hep-ph↗

arXiv2014

Estimation of electric conductivity of the quark gluon plasma via asymmetric heavy-ion collisions

We show that in asymmetric heavy-ion collisions, especially off-central Cu+Au collisions, a sizable strength of electric field directed from Au nucleus to Cu nucleus is generated in the overlapping region, because of the difference in the number of electric charges between the two nuclei. This electric field would induce an electric current in the matter created after the collision, which result in a dipole deformation of the charge distribution. The directed flow parameters $v_1^{\pm}$ of charged particles turn out to be sensitive to the charge dipole and provide us with information about electric conductivity of the quark gluon plasma.

nucl-th↗