Single-particle Entanglement of the Entanglement Hamiltonian Eigen-modes

TL;DR

This paper investigates single-particle entanglement entropy (SPEE) of entanglement Hamiltonian eigen-modes in a 1D free fermion model, revealing its potential as a phase transition indicator between delocalized and localized phases.

Contribution

It demonstrates that SPEE of entanglement Hamiltonian eigen-modes mirrors Hamiltonian eigen-modes behavior and sharply signals phase transitions, introducing a new phase detection method.

Findings

SPEE decreases as the system transitions from delocalized to localized phase.

Fluctuations of SPEE sharply indicate the phase transition point.

SPEE and SPRE serve as effective phase detection parameters.

Abstract

Single-particle entanglement entropy (SPEE) is calculated for entanglement Hamiltonian eigen-mode in a one-dimensional free fermion model that undergoes a delocalized-localized phase transition. In this numerical study, we show that SPEE of entanglement Hamiltonian eigen-mode has the same behavior as EPEE of Hamiltonian eigen-mode at the Fermi level: as we go from delocalized phase toward localized phase, SPEE of both modes decreases in the same manner. Furthermore, fluctuations of SPEE of entanglement Hamiltonian eigen-mode -- which can be obtained through the calculation of moments of SPEE -- signature very sharply the phase transition point. These two modes are also compared by calculation of single particle R\'{e}yni entropy (SPRE). We show that SPEE and SPRE of entanglement Hamiltonian eigen-mode can be used as a phase detection parameter.