Specific heat and density anomaly in the Hubbard model
Phys. Rev. B 113, 165111 – Published 8 April, 2026
DOI: https://doi.org/10.1103/6t32-g4cr
Abstract
Understanding thermal properties of materials is fundamental to technological applications and to discovering new phenomena. In particular, advances in experimental techniques such as cold-atom measurements allow the simulation of paradigmatic Hamiltonians with great control over model parameters, such as the Hubbard model. One aspect of this model which is not much explored is the behavior of the specific heat as a function of density. In this work, we perform determinant quantum Monte Carlo simulations of the Hubbard model interpolating between the square and triangular lattices to analyze the specific heat as the filling, interaction, and temperature of the system are changed. We found that, with strong correlations, the specific heat presents a three-maxima structure as a function of filling, with local minima between them. This effect can be explained by a decomposition of kinetic and potential contributions to the specific heat, demonstrating interesting phenomena away from the commonly studied half-filling regime. Moreover, by analyzing the kinetic contribution in momentum space we show that, connected to this specific heat behavior, there is a density anomaly detected through the thermal expansion coefficient. These momentum-space quantities are accessible using cold-atom experimental measurements at multiple temperatures. Finally, we map the location of these phenomena and connect the thermal expansion anomaly with the well-known Seebeck coefficient change of sign. Our results provide an alternative perspective to analyze this change of sign.
