Clustering Theorem for Bose-Hubbard class Gibbs states

TL;DR

This paper proves exponential decay of correlations in high-temperature Bose-Hubbard Gibbs states, providing analytical insights into low-density conditions and thermal properties of bosonic systems.

Contribution

It introduces a novel interaction-picture cluster-expansion technique to handle unbounded bosonic operators and establish clustering in Bose-Hubbard models.

Findings

Exponential clustering of correlations in high-temperature regimes

Bound on the specific heat density

Bosonic thermal area law with improved temperature dependence

Abstract

We establish the exponential clustering of correlation functions for the high-temperature Gibbs states of Bose-Hubbard type models. To overcome the technical difficulties arising from the unboundedness of bosonic operators, we develop the interaction-picture cluster-expansion technique. This method also allows us to systematically bound the moments of the local particle number. This result provides an analytical justification for the low-boson-density condition frequently assumed in the study of bosonic many-body systems. As direct mathematical consequences of the clustering property, we derive a uniform upper bound on the specific heat density and establish a bosonic thermal area law with improved temperature dependence.