Temperature and Density Dependence of the 2D Hubbard Model Entropy at Intermediate to High Temperatures

The entropy of the 2D Hubbard Model on a square lattice has a crossover at intermediate temperatures due to the growing importance of strong on-site repulsion as the temperature is lowered. At high temperatures T» U the density derivative of the entropy ∂S/∂n at fixed temperature is zero at half filling, indicating the entropy has a maximum as a function of density at half filling, like the non-interacting tight binding model. For large U as the temperature is reduced there is a sharp temperature where the density dependence of the entropy at half filling goes from a maximum to a local minimum, with ∂S/∂n¦_T = ∂μ/∂T¦_n = 0 for all temperatures, since μ = U/2 is temperature independent at half filling. The maximum in the entropy as a function of density shifts smoothly on both sides of half filling to n = 2/3 and n = 4/3 at intermediate temperatures below the sharp change in behavior at half filling. The entropy having a maximum as a function of density at n = 2/3 agrees with the high temperature behavior of the t-J model and is an unambiguous sign of strong electronic correlations.