Odd-flavor Simulations by the Hybrid Monte Carlo

TL;DR

This paper explores simulating odd-flavor QCD using an adapted hybrid Monte Carlo algorithm with polynomial approximation, comparing its results to the R-algorithm and demonstrating consistency at small step sizes.

Contribution

It introduces a method for simulating odd-flavor QCD with hybrid Monte Carlo and compares its accuracy to the R-algorithm.

Findings

Hybrid Monte Carlo results agree with R-algorithm at small step sizes.

The polynomial approximation enables odd-flavor simulations.

The method provides a viable alternative for odd-flavor QCD simulations.

Abstract

The standard hybrid Monte Carlo algorithm is known to simulate even flavors QCD only. Simulations of odd flavors QCD, however, can be also performed in the framework of the hybrid Monte Carlo algorithm where the inverse of the fermion matrix is approximated by a polynomial. In this exploratory study we perform three flavors QCD simulations. We make a comparison of the hybrid Monte Carlo algorithm and the R-algorithm which also simulates odd flavors systems but has step-size errors. We find that results from our hybrid Monte Carlo algorithm are in agreement with those from the R-algorithm obtained at very small step-size.