We study the thermodynamics of the two-dimensional Hubbard model within the dynamical cluster approximation. We use continuous time quantum Monte Carlo as a cluster solver to avoid the systematic error which complicates the calculation of the entropy and potential energy (double occupancy). We find that at a critical filling, there is a pronounced peak in the entropy divided by temperature, S/T, and in the normalized double occupancy as a function of doping. At this filling, we find that specific heat divided by temperature, C/T, increases strongly with decreasing temperature and kinetic and potential energies vary like T2 ln T. These are all characteristics of quantum critical behavior.
K. Mikelsons, Ehsan Khatami, D. Galanakis, A. Macridin, J. Moreno, and M. Jarrell. "Thermodynamics of the quantum critical point at finite doping in the two-dimensional Hubbard model studied via the dynamical cluster approximation" Physical Review B (2009). doi:10.1103/PhysRevB.80.140505