A modified Cayley transform for SU(3) molecular dynamics simulations

TL;DR

This paper introduces a modified Cayley transform for SU(3) that improves Hamiltonian simulation methods, especially in lattice QCD, by maintaining key properties like time-reversibility and volume preservation.

Contribution

The paper develops a new Cayley transform for SU(3) that enhances splitting methods for Hamiltonian systems, with applications to lattice QCD simulations.

Findings

The modified Cayley transform preserves time-reversibility.

It maintains volume-preservation in splitting methods.

Demonstrated advantages in pure gauge field simulations.

Abstract

We propose a modification to the Cayley transform that defines a suitable local parameterization for the special unitary group $\mathrm{SU}(3)$. The new mapping is used to construct splitting methods for separable Hamiltonian systems whose phase space is the cotangent bundle of $\mathrm{SU}(3)$ or, more general, $\mathrm{SU(3)}^N$, $N \in \mathbb{N}$. Special attention is given to the hybrid Monte Carlo algorithm for gauge field generation in lattice quantum chromodynamics. We show that the use of the modified Cayley transform instead of the matrix exponential neither affects the time-reversibility nor the volume-preservation of the splitting method. Furthermore, the advantages and disadvantages of the Cayley-based algorithms are discussed and illustrated in pure gauge field simulations.