Specific heat and density anomaly in the Hubbard model

TL;DR

This study uses Quantum Monte Carlo simulations to explore the specific heat and density anomalies in the Hubbard model, revealing a three-peak structure and associated thermal expansion phenomena.

Contribution

It uncovers a three-maxima structure in specific heat as a function of filling and links it to density anomalies and thermoelectric properties.

Findings

Specific heat exhibits three maxima with local minima at certain fillings.

Density anomalies are connected to the kinetic contribution in momentum space.

Thermal expansion coefficient changes sign, correlating with the Seebeck coefficient.

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 experiments 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 a new perspective to analyze this change of sign.