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

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