Quantum Criticality and Incipient Phase Separation in the Thermodynamic Properties of the Hubbard Model

TL;DR

This study provides numerical evidence for a quantum critical point in the Hubbard model, linking Fermi-liquid and pseudogap states, and suggests a phase separation transition related to quantum criticality in cuprates.

Contribution

It demonstrates the existence of a quantum critical point in the extended Hubbard model through dynamical cluster quantum Monte Carlo simulations, connecting different electronic phases.

Findings

Identification of a crossover from Fermi liquid to pseudogap state.

Existence of a classical critical point associated with phase separation.

Marginal Fermi-liquid behavior near the quantum critical point.

Abstract

Transport measurements on the cuprates suggest the presence of a quantum critical point hiding underneath the superconducting dome near optimal hole doping. We provide numerical evidence in support of this scenario via a dynamical cluster quantum Monte Carlo study of the extended two-dimensional Hubbard model. Single particle quantities, such as the spectral function, the quasiparticle weight and the entropy, display a crossover between two distinct ground states: a Fermi liquid at low filling and a non-Fermi liquid with a pseudogap at high filling. Both states are found to cross over to a marginal Fermi-liquid state at higher temperatures. For finite next-nearest-neighbor hopping t' we find a classical critical point at temperature T_c. This classical critical point is found to be associated with a phase separation transition between a compressible Mott gas and an incompressible Mott liquid corresponding to the Fermi liquid and the pseudogap state, respectively. Since the critical temperature T_c extrapolates to zero as t' vanishes, we conclude that a quantum critical point connects the Fermi-liquid to the pseudogap region, and that the marginal-Fermi-liquid behavior in its vicinity is the analogous of the supercritical region in the liquid-gas transition.