Sensitivity of the entanglement spectrum to boundary conditions as a characterization of the phase transition from delocalization to localization

TL;DR

This paper demonstrates that the sensitivity of the entanglement spectrum to boundary conditions effectively detects phase transitions from delocalized to localized states and can identify mobility edges in one-dimensional models.

Contribution

It introduces a novel method using entanglement spectrum shifts under boundary condition changes to identify phase transition points and mobility edges.

Findings

Entanglement energy shifts change significantly at the transition point.

Entanglement entropy shifts serve as indicators of phase transition.

Method can determine mobility edges separating localized and delocalized states.

Abstract

Sensitivity of entanglement Hamiltonian spectrum to boundary conditions is considered as a phase detection parameter for delocalized-localized phase transition. By employing one-dimensional models that undergo delocalized-localized phase transition, we study the shift in the entanglement energies and the shift in the entanglement entropy when we change boundary conditions from periodic to anti-periodic. Specifically, we show that both these quantities show a change of several orders of magnitude at the transition point in the models considered. Therefore, this shift can be used to indicate the phase transition points in the models. We also show that both these quantities can be used to determine \emph{mobility edges} separating localized and delocalized states.