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 th
e negative sign problem. We analyze the antiferromagnetic order and its suppression by the non-Hermiticity.
The simulation of dense fermionic matters is a long-standing problem in lattice gauge theory. One hopeful solution would be the use of quantum computers. In this paper, digital quantum simulation is designed for lattice gauge theory at nonzero densit
y. The quantum variational algorithm is adopted to obtain the ground state at nonzero density. A benchmark test is performed in the lattice Schwinger model.
This is an introductory review of lattice QCD with external fields. The study of external magnetic fields is one of the greatest achievements in modern lattice QCD. Large-scale simulations and detailed analyses have revealed intriguing properties of
QCD in the magnetic fields. The study of external electric fields is more challenging because of a technical difficulty. We overview the successes and challenges of the lattice simulations with the electromagnetic fields. We also introduce a newly developing field, the lattice simulation of rotating QCD matters.
We study the quantum simulation of Z2 lattice gauge theory in 2+1 dimensions. The dual variable formulation, the so-called Wegner duality, is utilized for reducing redundant gauge degrees of freedom. The problem of artificial charge unconservation is
resolved for any charge distribution. As a demonstration, we simulate the real-time evolution of the system with two static electric charges, i.e., with two temporal Wilson lines. Some results obtained by the simulator (with no hardware noise) and the real device (with sizable hardware noise) of a quantum computer are shown.
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 v
alue 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.
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.
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 f
or 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.
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 th
e 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.
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 spatia
l distribution of non-Abelian vortices suggests the repulsive vortex-vortex interaction.
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 f
ields with many-body interaction. We derive the path integral representation and perform the lattice Monte Carlo simulation.
