Extended framework for the hybrid Monte Carlo in lattice gauge theory

TL;DR

This paper introduces an extended hybrid Monte Carlo framework for lattice gauge theory by embedding the gauge group into complex matrices, allowing for non-separable Hamiltonians and improved flexibility in simulations.

Contribution

The authors develop a novel embedding of the $SU(N)$ group into complex matrices, enabling non-separable Hamiltonians and expanding the capabilities of HMC in lattice gauge theory.

Findings

Embedding preserves original expectation values.

Allows for non-separable Hamiltonians.

Enables Riemannian manifold HMC applications.

Abstract

We develop an extended framework for the hybrid Monte Carlo (HMC) algorithm in lattice gauge theory by embedding the $SU(N)$ group into the space of general complex matrices,$M_N(\mathbb{C})$. Auxiliary directions will be completely factorized in the path integral, and the embedding does not alter the expectation values of the original theory. We perform the molecular dynamics updates by using the matrix elements of $W \in M_N(\mathbb{C})$ as the dynamical variables without group theoretic constraints. The framework enables us to introduce non-separable Hamiltonians for the HMC in lattice gauge theory exactly, whose immediate application includes the Riemannian manifold HMC.