One-Flavour Hybrid Monte Carlo with Wilson Fermions

TL;DR

This paper introduces a novel hybrid Monte Carlo method for simulating Wilson fermions with non-degenerate quark flavors, effectively handling nested inversions through a new Uzawa iteration scheme.

Contribution

The paper presents a new formulation of the Wilson fermion determinant and a Uzawa iteration scheme to efficiently manage nested inversions in hybrid Monte Carlo simulations.

Findings

Successful implementation of the Uzawa iteration scheme

Efficient simulation of non-degenerate quark flavors

Reduction in computational complexity of nested inversions

Abstract

The Wilson fermion determinant can be written as product of the determinants of two hermitian positive definite matrices. This formulation allows to simulate non-degenerate quark flavors by means of the hybrid Monte Carlo algorithm. A major numerical difficulty is the occurrence of nested inversions. We construct a Uzawa iteration scheme which treats the nested system within one iterative process.