The RHMC algorithm for theories with unknown spectral bounds

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.

Latex(Revtex 4) 25 pages, 8 postscript figures

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Cited by in corpus (6)

• Study of the finite temperature transition in 3-flavor QCD using the R and RHMC algorithms
• Lattice QCD at finite temperature and density in the phase-quenched approximation
• Separating the scales of confinement and chiral-symmetry breaking in lattice QCD with fundamental quarks
• Phase Quenched Lattice QCD at Finite Density and Temperature
• Lattice QCD at finite density: imaginary chemical potential
• Recent algorithm and machine developments for lattice QCD