New One-Flavor Hybrid Monte Carlo Simulation Method for Lattice Fermions with gamma-five Hermiticity

TL;DR

This paper introduces a novel Hybrid Monte Carlo method for simulating odd numbers of lattice fermions, leveraging gamma-five hermiticity, applicable to various fermion formulations, and demonstrating improved efficiency in simulations.

Contribution

The paper presents a new HMC approach that differs from polynomial or rational methods, utilizing gamma-five hermiticity for more efficient simulations of lattice fermions.

Findings

Efficiency ratio of about 3:2 in simulations

Applicable to Wilson, domain-wall, and overlap fermions

Analyzes relation between pseudofermion actions in different representations

Abstract

We propose a new method for Hybrid Monte Carlo (HMC) simulations with odd numbers of dynamical fermions on the lattice. It employs a different approach from polynomial or rational HMC. In this method, gamma-five hermiticity of the lattice Dirac operators is crucial and it can be applied to Wilson, domain-wall, and overlap fermions. We compare HMC simulations with two degenerate flavors and (1 + 1) degenerate flavors using optimal domain-wall fermions. The ratio of the efficiency, (number of accepted trajectories) / (simulation time), is about 3:2. The relation between pseudofermion action of chirally symmetric lattice fermions in four-dimensional(overlap) and five-dimensional(domain-wall) representation are also analyzed.