New one-flavor hybrid Monte Carlo simulation method for lattice fermions with [formula omitted] hermiticity

Kenji Ogawa

doi:10.1016/j.physletb.2011.09.023

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, γ5 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.

Highlights

In hybrid Monte Carlo simulations [1], the positive-definiteness of the action is essential to consider it as the statistical weight
We provide a pseudofermion action for the one flavor sector of the lattice fermions with γ5 hermiticity without invoking the square root approximation for D†D
The largest difference of the method presented here from RHMC and PHMC is that the pseudofermion action yields the one-flavor determinant without any approximations

Summary

Introduction

In hybrid Monte Carlo simulations [1], the positive-definiteness of the action is essential to consider it as the statistical weight. When a lattice Dirac operator D is given, a positive-definite action of two degenerate flavors is constructed by using the hermitian conjugate of D, namely D†D. Rational or polynomial HMC methods [2, 3], which approximates the square root of D†D, are mostly used for odd flavor simulations. We provide a pseudofermion action for the one flavor sector of the lattice fermions with γ5 hermiticity without invoking the square root approximation for D†D. For any lattice Dirac operators D with γ5 hermiticity, P+DP+ and P−(1/D)P− are hermitian, and one can construct a one-flavor pseudofermion action using these. The non-trivial parts are to first check the positive-definiteness of the pseudofermion action and the discussion of how to obtain the pseudofermion action when there are mass preconditioners like the one in Hasenbusch method.

Wilson Fermions

Wilson fermions with the Hasenbusch method

Domain-wall fermions

Overlap Fermions

Numerical tests

Concluding remarks