Double-peak specific heat anomaly and correlations in the Bose-Hubbard model

TL;DR

This paper investigates the double-peak anomalies in the specific heat of the Bose-Hubbard model, revealing their origins in energetic competition and ground-state degeneracies through advanced theoretical methods.

Contribution

It introduces a mechanism explaining double-peak specific heat features in the Bose-Hubbard model based on residual entropies and spectral analysis, expanding understanding of thermodynamic anomalies.

Findings

Double peaks linked to energetic competition and degeneracies.

Spectral properties influence the structure of specific heat peaks.

Correlation functions reveal the nature of the thermodynamic anomalies.

Abstract

Considering the thermodynamics of bosons in a lattice described by the Bose-Hubbard Hamiltonian, we report the occurrence of anomalous double peaks in their specific heat dependence on temperature. This feature, usually associated with a high geometrical frustration, can also be a consequence of a purely energetic competition. By employing self-energy functional calculations combined with finite-temperature perturbation theory, we propose a mechanism based on ground-state degeneracies expressed as residual entropies. A general decomposition of the specific heat regarding all possible transitions between the system's eingenvalues provides an insight into the nature of each maximum. Furthermore, we address how the model parameters modify the structure of these peaks based on its spectral properties and atom-atom correlation function.