arXiv subjects

Takanori Sugihara

Publications and source records attributed to Takanori Sugihara.

18 recordsLinked to original sources

arXiv2014

Local representation of N-body Coulomb energy with path integrals

We represent N-body Coulomb energy in a localized form to achieve massive parallelism. It is a well-known fact that Green's functions can be written as path integrals of field theory. Since two-body Coulomb potential is a Green's function of Poisson equations, it reduces to a path integral of free scalar field theory with three spatial dimensions. This means that N-body one also reduces to a path integral. We discretize real space with a cubic lattice and evaluate the obtained multiple integrals approximately with the Markov-chain Monte Carlo method.

physics.comp-ph↗

arXiv2009

Parallelization of Markov chain generation and its application to the multicanonical method

We develop a simple algorithm to parallelize generation processes of Markov chains. In this algorithm, multiple Markov chains are generated in parallel and jointed together to make a longer Markov chain. The joints between the constituent Markov chains are processed using the detailed balance. We apply the parallelization algorithm to multicanonical calculations of the two-dimensional Ising model and demonstrate accurate estimation of multicanonical weights.

cond-mat.stat-mech↗

arXiv2005

Gauge invariance in a Z_2 hamiltonian lattice gauge theory

We propose an efficient variational method for $Z_2$ lattice gauge theory based on the matrix product ansatz. The method is applied to ladder and square lattices. The Gauss law needs to be imposed on quantum states to guarantee gauge invariance when one studies gauge theory in hamiltonian formalism. On the ladder lattice, we identify gauge invariant low-lying states by evaluating expectation values of the Gauss law operator after numerical diagonalization of the gauge hamiltonian. On the square lattice, the second order phase transition is well reproduced.

hep-lat↗

arXiv2005

Matrix product representation of gauge invariant states in a Z_2 lattice gauge theory

The Gauss law needs to be imposed on quantum states to guarantee gauge invariance when one studies gauge theory in hamiltonian formalism. In this work, we propose an efficient variational method based on the matrix product ansatz for a Z_2 lattice gauge theory on a spatial ladder chain. Gauge invariant low-lying states are identified by evaluating expectation values of the Gauss law operator after numerical diagonalization of the gauge hamiltonian.

hep-lat↗

arXiv2004

Matrix product variational formulation for lattice gauge theory

For hamiltonian lattice gauge theory, we introduce the matrix product anzats inspired from density matrix renormalization group. In this method, wavefunction of the target state is assumed to be a product of finite matrices. As a result, the energy becomes a simple function of the matrices, which can be evaluated using a computer. The minimum of the energy function corresponds to the vacuum state. We show that the S=1/2 Heisenberg chain model are well described with the ansatz. The method is also applied to the two-dimensional S=1/2 Heisenberg and U(1) plaquette chain models.

hep-lat↗

arXiv2004

Density matrix renormalization group approach to a two-dimensional bosonic model

Density matrix renormalization group (DMRG) is applied to a (1+1)-dimensional $λϕ^4$ model to study spontaneous breakdown of discrete $Z_2$ symmetry numerically. We obtain the critical coupling $(λ/μ^2)_{\rm c}=59.89\pm 0.01$ and the critical exponent $β=0.1264\pm 0.0073$, which are consistent with the Monte Carlo and the exact results, respectively. The results are based on extrapolation to the continuum limit with lattice sizes $L=250,500$, and 1000. We show that the lattice size L=500 is sufficiently close to the the limit $L\to\infty$ \cite{Sugihara:2004qr}.

hep-lat↗

arXiv2004

Density matrix renormalization group in a two-dimensional $λϕ^4$ Hamiltonian lattice model

Density matrix renormalization group (DMRG) is applied to a (1+1)-dimensional $λϕ^4$ model. Spontaneous breakdown of discrete $Z_2$ symmetry is studied numerically using vacuum wavefunctions. We obtain the critical coupling $(λ/μ^2)_{\rm c}=59.89\pm 0.01$ and the critical exponent $β=0.1264\pm 0.0073$, which are consistent with the Monte Carlo and the exact results, respectively. The results are based on extrapolation to the continuum limit with lattice sizes $L=250,500$, and 1000. We show that the lattice size L=500 is sufficiently close to the the limit $L\to\infty$.

hep-lat↗

arXiv2004

Vector and chiral gauge theories on the lattice

We combine a pair of independent Weyl fermions to compose a Dirac fermion on the four-dimensional Euclidean lattice. The obtained Dirac operator is antihermitian and does not reproduce anomaly under the usual chiral transformation. To simulate the correct chiral anomaly, we modify the chiral transformation. We also show that chiral gauge theories can be constructed nonperturbatively with exact gauge invariance. The formulation is based on a doubler-free lattice derivative, which is a simple matrix defined as a discrete Fourier transform of momentum with antiperiodic boundary conditions. Long-range fermion hopping interactions are truncated using the Lanczos factor.

hep-lat↗

arXiv2004

Basis Optimization Renormalization Group for Quantum Hamiltonian

We find an algorithm of numerical renormalization group for spin chain models. The essence of this algorithm is orthogonal transformation of basis states, which is useful for reducing the number of relevant basis states to create effective Hamiltonian. We define two types of rotations and combine them to create appropriate orthogonal transformation.

hep-th↗

arXiv2004

Lattice representation of vector and chiral gauge theories

A lattice derivative is defined as a discrete Fourier transform of momentum on a finite lattice. Species doublers are removed with anti-periodic boundary conditions. U(1) chiral transformation is modified to reproduce chiral anomaly. Chiral gauge theories can be constructed on the lattice using a single Weyl fermion as a building block.

hep-lat↗

arXiv2003

Chiral symmetry on a lattice with hopping interactions

The species doubling problem of the lattice fermion is resolved by introducing hopping interactions that mix left- and right-handed fermions around the momentum boundary. Approximate chiral symmetry is realized on the lattice. The deviation of the fermion propagator from the continuum one is small.

hep-lat↗

arXiv2003

Lattice chiral symmetry with hopping interactions

We formulate Dirac fermions on a (1+1)-dimensional lattice based on a Hamiltonian formalism. The species doubling problem of the lattice fermion is resolved by introducing hopping interactions that mix left- and right-handed fermions around the momentum boundary. Approximate chiral symmetry is realized on the lattice. The deviation of the fermion propagator from the continuum one is small.

hep-lat↗

arXiv2001

Manifestation of a nontrivial vacuum in discrete light cone quantization

We study a (1+1)-dimensional $λϕ^4$ model with a light-cone zero mode and constant external source to describe spontaneous symmetry breaking. In the broken phase, we find degenerate vacua and discuss their stability based on effective-potential analysis. The vacuum triviality is spurious in the broken phase because these states have lower energy than Fock vacuum. Our results are based on the variational principle.

hep-th↗

arXiv1998

Variational Calculation of the Effective Action

An indication of spontaneous symmetry breaking is found in the two-dimensional $λϕ^4$ model, where attention is paid to the functional form of an effective action. An effective energy, which is an effective action for a static field, is obtained as a functional of the classical field from the ground state of the hamiltonian $H[J]$ interacting with a constant external field. The energy and wavefunction of the ground state are calculated in terms of DLCQ (Discretized Light-Cone Quantization) under antiperiodic boundary conditions. A field configuration that is physically meaningful is found as a solution of the quantum mechanical Euler-Lagrange equation in the $J\to 0$ limit. It is shown that there exists a nonzero field configuration in the broken phase of $Z_2$ symmetry because of a boundary effect.

hep-th↗

arXiv1996

Nonperturbative renormalization group in a light-front three-dimensional real scalar model

The three-dimensional real scalar model, in which the $Z_2$ symmetry spontaneously breaks, is renormalized in a nonperturbative manner based on the Tamm-Dancoff truncation of the Fock space. A critical line is calculated by diagonalizing the Hamiltonian regularized with basis functions. The marginal ($ϕ^6$) coupling dependence of the critical line is weak. In the broken phase the canonical Hamiltonian is tachyonic, so the field is shifted as $ϕ(x)\toφ(x)+v$. The shifted value $v$ is determined as a function of running mass and coupling so that the mass of the ground state vanishes.

hep-th↗

arXiv1995

A perturbative renormalization group approach to light-front Hamiltonian

A perturbative renormalization group (RG) scheme for light-front Hamiltonian is formulated on the basis of the Bloch-Horowitz effective Hamiltonian, and applied to the simplest $ϕ^4$ model with spontaneous breaking of the $Z_2$ symmetry. RG equations are derived at one-loop order for both symmetric and broken phases. The equations are consistent with those calculated in the covariant perturbation theory. For the symmetric phase, an initial cutoff Hamiltonian in the RG procedure is made by excluding the zero mode from the canonical Hamiltonian with an appropriate regularization. An initial cutoff Hamiltonian for the broken phase is constructed by shifting $ϕ$ as $ϕ\rightarrowϕ-v$ in the initial Hamiltonian for the symmetric phase. The shifted value $v$ is determined on a renormalization trajectory. The minimum of the effective potential occurs on the trajectory.

hep-th↗

arXiv1994

Two-dimensional SU(N) Gauge Theory on the Light Cone

Two-dimensional SU($N$) gauge theory is accurately analyzed with the light-front Tamm-Dancoff approximation, both numerically and analytically. The light-front Einstein-Schrödinger equation for mesonic mass reduces to the 't Hooft equation in the large $N$ limit, $g^2N$ fixed, where $g$ is the coupling constant. Hadronic masses are numerically obtained in the region of $m^2 \ll g^2N$, where $m$ is the bare quark (q) mass. The lightest mesonic and baryonic states are almost in valence. The second lightest mesonic state is highly relativistic in the sense that it has a large 4-body ($ {\rm qq} \bar{\rm q} \bar{\rm q} $) component in addition to the valence (${\rm q} \bar{\rm q}$) one. In the strong coupling limit our results are consistent with the prediction of the bosonization for ratios of the lightest and second lightest mesonic masses to the lightest baryonic one. Analytic solutions to the lightest hadronic masses are obtained, with a reasonable approximation, as $\sqrt{2Cm}(1-1/N^2)^{1/4}$ in the mesonic case and $\sqrt{CmN(N-1)}(1-1/N^2)^{1/4}$ in the baryonic case, where $C=(g^2Nπ/6)^{1/2}$. The solutions well reproduce the numerical ones. The $N$- and $m$-dependences of the hadronic masses are explicitly shown by the analytical solutions.

hep-th↗

arXiv1993

The massive Schwinger model with $SU(2)_{f}$ on the light cone

The massive Schwinger model with two flavors is studied in the strong coupling region by using light-front Tamm-Dancoff approximation. The mass spectrum of the lightest particles is obtained numerically. We find that the mass of the lightest isotriplet (``pion'') behaves as $m^{0.50}$ for the strong couplings, where $m$ is the fermion mass. We also find that the lightest isosinglet is not in the valence state (``eta'') which is much heavier in the strong coupling region, but can be interpreted as a bound state of two pions. It is 1.762 times heavier than pion at $m=1.0\times10^{-3}(e/\sqrtπ)$, while Coleman predicted that the ratio is $\sqrt3$ in the strong coupling limit. The ``pion decay constant'' is calculated to be 0.3945.

hep-th↗