Quasilocal entanglement across the Mott-Hubbard transition

TL;DR

This paper investigates the Mott-Hubbard transition in the 2D Hubbard model using quasilocal entanglement measures, revealing the importance of nearest-neighbor entanglement in characterizing Mott localization.

Contribution

It introduces a quasilocal entanglement framework to analyze the Mott transition, providing new insights beyond traditional single-site entropy approaches.

Findings

Nearest-neighbor entanglement sharply increases at the transition

Two-site entanglement diminishes rapidly with distance

Single-site von Neumann entropy decreases monotonically with interaction

Abstract

The possibility to directly measure, in a cold-atom quantum simulator, the von Neumann entropy and mutual information between a site and its environment opens new perspectives on the characterization of the Mott-Hubbard metal-insulator transition, in the framework of quantum information theory. In this work we provide an alternative view of the Mott transition in the two-dimensional Hubbard model in terms of rigorous quasilocal measures of entanglement and correlation between two spatially separated electronic orbitals, with no contribution from their environment. A space-resolved analysis of cluster dynamical mean-field theory results elucidates the prominent role of the nearest-neighbor entanglement in probing Mott localization: both its lower and upper bounds sharply increase at the metal-insulator transition. The two-site entanglement beyond nearest neighbors is shown to be quickly damped as the inter-site distance is increased. These results ultimately resolve a conundrum of previous analyses based on the single-site von Neumann entropy, which has been found to monotonically decrease when the interaction is increased. The quasilocal two-site entanglement recovers instead the distinctive character of Mott insulators as strongly correlated quantum states, demonstrating its central role in the $2d$ Hubbard model.