Precursors of the insulating state in the square-lattice Hubbard model

Abstract

We study the two-dimensional square-lattice Hubbard model for small to moderate interaction strengths $1\ensuremath{\le}U/t\ensuremath{\le}4$ by means of the ladder dual fermion approach. The nonlocal correlations beyond dynamical mean-field theory lower the potential energy, lead to a maximum in the uniform susceptibility, and induce a pseudogap in the density of states. While the self-energy exhibits precursors of a possible insulating phase linked to the appearance of long-range fluctuations, the metallic phase persists within the accessible temperature range. Finite-size effects affect results qualitatively. Upper bounds on the crossover temperature are found to be significantly lower than previously reported dynamical vertex approximation results at $U/t=1$.