Thermodynamics of the quantum critical point at finite doping in the two-dimensional Hubbard model studied via the dynamical cluster approximation

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 $T^2 \ln T$. These are all characteristics of quantum critical behavior.