Clustering Theorem for Bose-Hubbard class Gibbs states

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.