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

Abstract

We study the thermodynamics of the two-dimensional Hubbard model within the dynamical cluster approxi mation. 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.

Evolution of the superconductivity dome in the two-dimensional Hubbard model

“…In this paper, we address the existence of a d-wave superconductivity dome in the Hubbard model directly using large-scale dynamical cluster quantum Monte Carlo simulations [9][10][11][12] . Based on the understanding obtained in this and previous numerical works 5,6,[13][14][15][16][17][18][19][20][21][22][23][24][25] , we furthermore map the evolution of the d-wave superconductivity dome in the parameter space of the phase diagram.…”

“…The two phases being separated are an incompressible Mott liquid and a compressible Mott gas; these two phases are adiabatically connected to the pseudogap and the Fermi liquid states at t ′ = 0. The first order line of coexis-tence terminates at a second order point where the charge susceptibility diverges 13,15,17,22 . As t ′ → 0, this critical point extrapolates continuously to zero temperature and thus becomes the quantum critical point (QCP) underneath the superconducting dome 21 .…”

Thermodynamics of strongly interacting fermions in two-dimensional optical lattices

“…Generally, when using QMC-based methods, entropy cal culations involve numerical derivatives and/or integration by parts [23,24], which can introduce systematic errors. Within U U NLCEs, the entropy is computed directly from its definition in the grand canonical ensemble:…”

Mott physics and first-order transition between two metals in the normal-state phase diagram of the two-dimensional Hubbard model

“…For example, the first-order transition was not detected at large values of the interaction by previous works most likely because the critical line moves rapidly to lower temperature with increasing interaction strength, falling below the temperatures accessible to date. Hence, previously reported features of the phase diagram of the Hubbard model 45,58,[64][65][66][67][68][69] , whether it is thermodynamic properties, scattering rate, momentum differentiation or other, appear in a different light. As we shall see, our analysis allows one to identify these features as precursors of the first-order transition, hence calling for their re-evaluation.…”

“…Recent investigations using this method and other continuous-time quantum Monte Carlo techniques 63 , have determined the interaction driven Mott MIT, revealing sharp modifications to the singlesite picture 38,39,41 . The transition driven by carrier concentration, more relevant for the high-temperature superconductors, is also currently under intense investigation 39,41,53,58,[64][65][66][67][68][69] . Motivated by the physics of the cuprates, almost all the studies focus on the large interaction regime where the Mott gap is well developed and they consider the effects of different band structure parameters in order to capture the striking particle-hole asymmetry observed in those compounds.…”