Non-Gibbs states on a Bose-Hubbard lattice

Abstract

We study the equilibrium properties of the repulsive quantum Bose-Hubbard model at high temperatures in arbitrary dimensions, with and without disorder. In its microcanonical setting the model conserves energy and particle number. The microcanonical dynamics is characterized by a pair of two densities: energy density E and particle number density n. The macrocanonical Gibbs distribution also depends on two parameters: the inverse non-negative temperature β and the chemical potential μ. We prove the existence of non-Gibbs states, that is, pairs (En) which cannot be mapped onto (β,μ). The separation line in the density control parameter space between Gibbs and non-Gibbs states E∼n2 corresponds to infinite temperature β=0. The non-Gibbs phase cannot be cured into a Gibbs one within the standard Gibbs formalism using negative temperatures. © 2019 American Physical Society