Entropy in the non-Fermi-liquid regime of the doped $2d$ Hubbard model

Abstract

We study thermodynamic properties of the doped Hubbard model on the square lattice in the regime of strong charge and spin fluctuations at low temperatures near the metal-to-insulator crossover and obtain results with controlled accuracy using the diagrammatic Monte Carlo method directly in the thermodynamic limit. The behavior of the entropy reveals a non-Fermi-liquid state at sufficiently high interactions near half-filling: a maximum in the entropy at non-zero doping develops as the coupling strength is increased, along with an inflection point, evidencing a metal to non-Fermi-liquid crossover. The specific heat exhibits additional distinctive features of a non-Fermi-liquid state. Measurements of the entropy can therefore be used as a probe of the state of the system in quantum simulation experiments with ultracold atoms in optical lattices.