Local Entanglement Entropy at the Mott Metal-Insulator Transition in Infinite Dimensions

TL;DR

This paper investigates the critical behavior of single-site entanglement entropy at the Mott transition in an infinite-dimensional Hubbard model, revealing exact and analytical results that characterize the transition's entanglement properties.

Contribution

It provides the first exact evaluation of entanglement entropy at the Mott transition in infinite dimensions using DMFT, combining numerical and analytical approaches.

Findings

Entanglement entropy scales logarithmically near the transition.

Exact and analytical methods agree on the entropy behavior.

Different coefficients on two sides of the transition.

Abstract

We study the critical behavior of the single-site entanglement entropy S at the Mott metal-insulator transition in infinite-dimensional Hubbard model. For this model, the entanglement between a single site and rest of the lattice can be evaluated exactly, using the dynamical mean-field theory (DMFT). Both the numerical solution using exact diagonalization and the analytical one using two-site DMFT gives S-Sc \propto \alpha \log_{2}[(1/2-Dc)/Dc](U-Uc), with Dc the double occupancy at Uc and \alpha < 0 being different on two sides of the transition.