arXiv subjects

Arata Yamamoto

Publications and source records attributed to Arata Yamamoto.

At least 37 records · Page 2Linked to original sources

arXiv2020

't Hooft surface in lattice gauge theory

We discuss the lattice formulation of the 't Hooft surface, that is, the two-dimensional surface operator of a dual variable. The 't Hooft surface describes the world sheets of topological vortices. We derive the formulas to calculate the expectation value of the 't Hooft surface in the multiple-charge lattice Abelian Higgs model and in the lattice non-Abelian Higgs model. As the first demonstration of the formula, we compute the intervortex potential in the charge-2 lattice Abelian Higgs model.

hep-lat↗

arXiv2020

Quantum Monte Carlo simulation of intervortex potential in superconductors

We investigate the interaction potential of superconducting vortices at the full quantum level. We formulate the interaction potential in a constrained path integral and calculate it by the quantum Monte Carlo simulation. The vortex-vortex potential is attractive (type-I), repulsive (type-II), and flat (critical) depending on a coupling constant. The vortex-antivortex potential also depends on the coupling constant at long range but is always attractive at short range.

cond-mat.supr-con↗

arXiv2019

String confinement in 2-form lattice gauge theory

We study the confinement between vortex strings in the dual lattice gauge theory of the abelian Higgs model. The dual lattice gauge theory is described by a 2-form gauge field. We calculate the string-antistring potential from the surface operator of the 2-form gauge field. The linear confining potential appears in a confinement phase and it disappears in a deconfinement phase. The phase diagram of the theory is also obtained.

hep-lat↗

arXiv2019

Lattice field theory with torsion

Inspired by the duality between gravity and defects in crystals, we study lattice field theory with torsion. The torsion is realized by a line defect of a lattice, namely a dislocation. As the first application, we perform the numerical computation for vector and axial currents induced by a screw dislocation. This current generation is called the chiral torsional effect. We also derive the analytical formula for the chiral torsional effect in the continuum limit.

hep-lat↗

arXiv2019

Meson deformation by magnetic fields in lattice QCD

We study light meson properties in a magnetic field, focusing on a charged pion and a charged and polarized rho meson, in quenched lattice QCD. The gauge-invariant density-density correlators are calculated to investigate the deformation caused by the magnetic field. We find that these mesons acquire elongated shapes along the magnetic field. The magnitude of the deformation is about 10-20 % when the strength of the magnetic field is of the order of the squared unphysical pion mass.

hep-lat↗

arXiv2018

Non-Abelian vortex in lattice gauge theory

We perform the Monte Carlo study of the SU(3) non-Abelian Higgs model. We discuss phase structure and non-Abelian vortices by gauge invariant operators. External magnetic fields induce non-Abelian vortices in the color-flavor locked phase. The spatial distribution of non-Abelian vortices suggests the repulsive vortex-vortex interaction.

hep-lat↗

arXiv2018

Abelian and non-Abelian Berry curvatures in lattice QCD

We studied the Berry curvature of the massive Dirac fermion in 3+1 dimensions. For the non-interacting Dirac fermion, the Berry curvature is non-Abelian because of the degeneracy of positive and negative helicity modes. We calculated the non-Abelian Berry curvature analytically and numerically. For the interacting Dirac fermion in QCD, the degeneracy is lost because gluons carry helicity and color charge. We calculated the Abelian Berry curvature in lattice QCD.

hep-lat↗

arXiv2018

One-dimensional anyons in relativistic field theory

We study relativistic anyon field theory in 1+1 dimensions. While (2+1)-dimensional anyon fields are equivalent to boson or fermion fields coupled with the Chern-Simons gauge fields, (1+1)-dimensional anyon fields are equivalent to boson or fermion fields with many-body interaction. We derive the path integral representation and perform the lattice Monte Carlo simulation.

hep-th↗

arXiv2017

Lattice simulation with the Majorana positivity

While the sign problem of the Dirac fermion is conditioned by the semi-positivity of a determinant, that of the Majorana fermion is conditioned by the semi-positivity 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

hep-lat↗

arXiv2017

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

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 semi-positive Pfaffian. We discuss spontaneous breaking of time-reversal symmetry at finite temperature.

cond-mat.str-el↗

arXiv2017

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

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.

hep-lat↗

arXiv2016

Quantum Monte Carlo simulation of topological phase transitions

We study the electron-electron interaction effects on topological phase transitions by the ab-initio quantum Monte Carlo simulation. We analyze two-dimensional class A topological insulators and three-dimensional Weyl semimetals with the long-range Coulomb interaction. The direct computation of the Chern number shows the electron-electron interaction modifies or extinguishes topological phase transitions.

cond-mat.mes-hall↗

arXiv2016

Lattice QCD simulation of the Berry curvature

The Berry curvature is a fundamental concept describing topological order of quantum systems. While it can be analytically tractable in non-interacting systems, numerical simulations are necessary in interacting systems. We present a formulation to calculate the Berry curvature in lattice QCD.

hep-lat↗

arXiv2016

Magnetism and rotation in relativistic field theory

We investigate the analogy between magnetism and rotation in relativistic theory. In nonrelativistic theory, the exact correspondence between magnetism and rotation is established in the presence of an external trapping potential. Based on this, we analyze relativistic rotation under external trapping potentials. A Landau-like quantization is obtained by considering an energy-dependent potential.

hep-th↗

arXiv2016

Berry phase in lattice QCD

We propose the lattice QCD calculation of the Berry phase which is defined by the ground state of a single fermion. We perform the ground-state projection of a single-fermion propagator, construct the Berry link variable on a momentum-space lattice, and calculate the Berry phase. As the first application, the first Chern number of the (2+1)-dimensional Wilson fermion is calculated by the Monte Carlo simulation.

hep-lat↗

arXiv2016

Nonrelativistic Banks-Casher relation and random matrix theory for multi-component fermionic superfluids

We apply QCD-inspired techniques to study nonrelativistic N-component degenerate fermions with attractive interactions. By analyzing the singular-value spectrum of the fermion matrix in the Lagrangian, we derive several exact relations that characterize the spontaneous symmetry breaking U(1)xSU(N)$\to$Sp(N) through bifermion condensates. These are nonrelativistic analogues of the Banks-Casher relation and the Smilga-Stern relation in QCD. Non-local order parameters are also introduced and their spectral representations are derived, from which a nontrivial constraint on the phase diagram is obtained. The effective theory of soft collective excitations is derived and its equivalence to random matrix theory is demonstrated in the epsilon-regime. We numerically confirm the above analytical predictions in Monte Carlo simulations.

cond-mat.quant-gas↗

arXiv2016

Quantum Monte Carlo simulation with a black hole

We perform quantum Monte Carlo simulations in the background of a classical black hole. The lattice discretized path integral is numerically calculated in the Schwarzschild metric and in its approximated metric. We study spontaneous symmetry breaking of a real scalar field theory. We observe inhomogeneous symmetry breaking induced by inhomogeneous gravitational field.

hep-lat↗

arXiv2015

Lifshitz-type SU(N) lattice gauge theory in five dimensions

We present a lattice formulation of non-Abelian Lifshitz-type gauge theories. Due to anisotropic scaling of space and time, the theory is asymptotically free even in five dimensions. We show results of Monte Carlo simulations that suggest a smooth approach to the continuum limit.

hep-lat↗