The RHMC algorithm for theories with unknown spectral bounds

TL;DR

The paper introduces an extension of the RHMC algorithm for lattice QCD simulations involving fractional powers of the Dirac operator, addressing spectral bound challenges and validating the method through specific QCD models.

Contribution

The paper develops a modified RHMC algorithm capable of handling unknown spectral bounds in certain lattice QCD theories, with validation against existing HMD simulations.

Findings

RHMC algorithm successfully applied to theories with unknown spectral bounds.

Comparison shows good agreement between RHMC and HMD results.

Choice of spectral bounds affects simulation properties, justified through comparisons.

Abstract

The Rational Hybrid Monte Carlo (RHMC) algorithm extends the Hybrid Monte Carlo algorithm for lattice QCD simulations to situations involving fractional powers of the determinant of the quadratic Dirac operator. This avoids the updating increment ($dt$) dependence of observables which plagues the Hybrid Molecular-dynamics (HMD) method. The RHMC algorithm uses rational approximations to fractional powers of the quadratic Dirac operator. Such approximations are only available when positive upper and lower bounds to the operator's spectrum are known. We apply the RHMC algorithm to simulations of 2 theories for which a positive lower spectral bound is unknown: lattice QCD with staggered quarks at finite isospin chemical potential and lattice QCD with massless staggered quarks and chiral 4-fermion interactions ($\chi$QCD). A choice of lower bound is made in each case, and the properties of the RHMC simulations these define are studied. Justification of our choices of lower bounds is made by comparing measurements with those from HMD simulations, and by comparing different choices of lower bounds.