Lattice meets lattice: Application of lattice cubature to models in lattice gauge theory

TL;DR

This paper develops recursive lattice cubature methods leveraging group structures and FFTs to efficiently compute high-dimensional integrals in lattice gauge theory models, with applications to quantum rotor and U(1) gauge theories.

Contribution

It introduces a novel application of lattice cubature rules combined with FFTs for high-dimensional integrals in quantum physics models.

Findings

Efficient recursive strategies for high-dimensional integrals.

Application to quantum rotor and U(1) lattice gauge models.

Potential computational benefits from group structure and FFTs.

Abstract

High dimensional integrals are abundant in many fields of research including quantum physics. The aim of this paper is to develop efficient recursive strategies to tackle a class of high dimensional integrals having a special product structure with low order couplings, motivated by models in lattice gauge theory from quantum field theory. A novel element of this work is the potential benefit in using lattice cubature rules. The group structure within lattice rules combined with the special structure in the physics integrands may allow efficient computations based on Fast Fourier Transforms. Applications to the quantum mechanical rotor and compact $U(1)$ lattice gauge theory in two and three dimensions are considered.