Hybrid Monte Carlo with Fat Link Fermion Actions

TL;DR

This paper introduces a differentiable projection method enabling Hybrid Monte Carlo simulations with fat link fermion actions, such as FLIC, in lattice QCD, overcoming previous non-differentiability issues.

Contribution

It presents a new projection technique that allows standard HMC algorithms to simulate dynamical fat link fermions, broadening the applicability of smearing methods in lattice QCD.

Findings

Derived equations of motion for FLIC fermions.

Implemented the projection technique in initial simulations.

Demonstrated compatibility with standard HMC algorithms.

Abstract

The use of APE smearing or other blocking techniques in lattice fermion actions can provide many advantages. There are many variants of these fat link actions in lattice QCD currently, such as FLIC fermions. The FLIC fermion formalism makes use of the APE blocking technique in combination with a projection of the blocked links back into the special unitary group. This reunitarisation is often performed using an iterative maximisation of a gauge invariant measure. This technique is not differentiable with respect to the gauge field and thus prevents the use of standard Hybrid Monte Carlo simulation algorithms. The use of an alternative projection technique circumvents this difficulty and allows the simulation of dynamical fat link fermions with standard HMC and its variants. The necessary equations of motion for FLIC fermions are derived, and some initial simulation results are presented. The technique is more general however, and is straightforwardly applicable to other smearing techniques or fat link actions.