Non-Gibbs states on a Bose-Hubbard lattice

TL;DR

This paper investigates the equilibrium properties of the Bose-Hubbard model at high temperatures, revealing the existence of non-Gibbs states that cannot be described by standard Gibbs distributions, especially at high energy and particle densities.

Contribution

It proves the existence of non-Gibbs states in the Bose-Hubbard model and characterizes the phase boundary between Gibbs and non-Gibbs states in the density space.

Findings

Non-Gibbs states exist in the Bose-Hubbard model at high temperatures.

The separation between Gibbs and non-Gibbs states occurs at infinite temperature.

Non-Gibbs phase cannot be transformed into Gibbs phase using negative temperatures.

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 $\varepsilon$ and particle number density $n$. The macrocanonical Gibbs distribution also depends on two parameters: the inverse nonnegative temperature $\beta$ and the chemical potential $\mu$. We prove the existence of non-Gibbs states, that is, pairs $(\varepsilon,n)$ which cannot be mapped onto $(\beta,\mu)$. The separation line in the density control parameter space between Gibbs and non-Gibbs states $\varepsilon \sim n^2$ corresponds to infinite temperature $\beta=0$. The non-Gibbs phase cannot be cured into a Gibbs one within the standard Gibbs formalism using negative temperatures.