Entanglement conductance as a characterization of delocalized-localized phase transition in free fermion models

TL;DR

This paper investigates how the structure of the entanglement Hamiltonian can distinguish between delocalized and localized phases in free fermion models, introducing entanglement conductance as a new phase transition indicator.

Contribution

It introduces entanglement conductance as a novel measure to characterize phase transitions in Anderson models, based on the structure of the entanglement Hamiltonian.

Findings

EH becomes long-range in delocalized phase

EH remains short-range in localized phase

Entanglement conductance effectively locates phase transition points

Abstract

We study entanglement Hamiltonian (EH) associated with the reduced density matrix of free fermion models in delocalized-localized Anderson phase transition. We show numerically that the structure of the EH matrix differentiates the delocalized from the localizedphase. In the delocalized phase, EH becomes a long-range Hamiltonian but is short-range in the localized phase, no matter what the configuration of the system's Hamiltonian is (whether it is long or short range). With this view, we introduce the entanglement conductance (EC), which quantifies how much EH is long-range and propose it as an alternative quantity to measure entanglement in the Anderson phase transition, by which we locate the phase transition point of some one-dimensional free fermion models; and also by applying the finite size method to the EC, we find three-dimensional Anderson phase transition critical disorder strength.