Large-time correlation functions in bosonic lattice field theories

TL;DR

This paper analyzes the statistical properties of large-time correlation functions in bosonic lattice field theories, showing how their deviations at large Euclidean times can reveal the theory's spectrum.

Contribution

It determines the asymptotic distribution of correlation functions in bosonic lattice theories and links deviations from this form to spectrum extraction.

Findings

Asymptotic distribution of correlation functions is derived.

Deviations from asymptotic form can be used to determine the spectrum.

Results apply to theories with a unique gapped vacuum.

Abstract

Large-time correlation functions have a pivotal role in extracting particle masses from Euclidean lattice field theory calculations, however little is known about the statistical properties of these quantities. In this work, the asymptotic form of the distributions of the correlation functions at vanishing momentum is determined for bosonic interacting lattice field theories with a unique gapped vacuum. It is demonstrated that the deviations from the asymptotic form at large Euclidean times can be utilized to determine the spectrum of the theory.