Entanglement and classical correlations at the doping-driven Mott transition in the two-dimensional Hubbard model

TL;DR

This study uses quantum information theory to analyze entanglement and correlations in the doped two-dimensional Hubbard model, revealing key phase transitions and the pseudogap phase through entanglement properties.

Contribution

It introduces a novel application of quantum information tools to identify phase transitions and the pseudogap phase in the doped Hubbard model.

Findings

Entanglement properties detect Mott insulator, pseudogap, and metallic phases.

Identifies first-order transition and critical endpoint of the pseudogap phase.

Reveals interplay of quantum and classical correlations at the transition.

Abstract

Tools of quantum information theory offer a new perspective to characterize phases and phase transitions in interacting many-body quantum systems. The Hubbard model is the archetypal model of such systems and can explain rich phenomena of quantum matter with minimal assumptions. Recent measurements of entanglement-related properties of this model using ultracold atoms in optical lattices hint that entanglement could provide the key to understanding open questions of the doped Hubbard model, including the remarkable properties of the pseudogap phase. These experimental findings call for a theoretical framework and new predictions. Here we approach the doped Hubbard model in two dimensions from the perspective of quantum information theory. We study the local entropy and the total mutual information across the doping-driven Mott transition within plaquette cellular dynamical mean-field theory. We find that upon varying doping these two entanglement-related properties detect the Mott insulating phase, the strongly correlated pseudogap phase, and the metallic phase. Imprinted in the entanglement-related properties we also find the pseudogap to correlated metal first-order transition, its finite temperature critical endpoint, and its supercritical crossovers. Through this footprint we reveal an unexpected interplay of quantum and classical correlations. Our work shows that sharp variation in the entanglement-related properties and not broken symmetry phases characterizes the onset of the pseudogap phase at finite temperature.