Polynomial Hybrid Monte Carlo algorithm for lattice QCD with an odd number of flavors

TL;DR

This paper introduces a polynomial hybrid Monte Carlo algorithm for lattice QCD with an odd number of flavors, demonstrating its efficiency and accuracy through extensive simulations and comparisons with existing methods.

Contribution

The paper develops a novel PHMC algorithm using Chebyshev polynomials for odd-flavor lattice QCD, including a new method to eliminate polynomial approximation errors.

Findings

Efficient for N_f=2 on large lattices with intermediate quark masses.

Works effectively for (2+1)-flavor QCD on small lattices.

Results agree with established algorithms, validating the new method.

Abstract

We present a polynomial hybrid Monte Carlo (PHMC) algorithm for lattice QCD with odd numbers of flavors of O(a)-improved Wilson quark action. The algorithm makes use of the non-Hermitian Chebyshev polynomial to approximate the inverse square root of the fermion matrix required for an odd number of flavors. The systematic error from the polynomial approximation is removed by a noisy Metropolis test for which a new method is developed. Investigating the property of our PHMC algorithm in the N_f=2 QCD case, we find that it is as efficient as the conventional HMC algorithm for a moderately large lattice size (16^3 times 48) with intermediate quark masses (m_{PS}/m_V ~ 0.7-0.8). We test our odd-flavor algorithm through extensive simulations of two-flavor QCD treated as an N_f = 1+1 system, and comparing the results with those of the established algorithms for N_f=2 QCD. These tests establish that our PHMC algorithm works on a moderately large lattice size with intermediate quark masses (16^3 times 48, m_{PS}/m_V ~ 0.7-0.8). Finally we experiment with the (2+1)-flavor QCD simulation on small lattices (4^3 times 8 and 8^3 times 16), and confirm the agreement of our results with those obtained with the R algorithm and extrapolated to a zero molecular dynamics step size.