Single-particle entanglement of the entanglement Hamiltonian eigenmodes

Abstract

Single-particle entanglement entropy (SPEE) is calculated for entanglement Hamiltonian eigenmode 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 Réyni entropy (SPRE). We show that SPEE and SPRE of entanglement Hamiltonian eigen-mode can be used as a phase detection parameter.

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

“…One special eigenvector of the U matrix, which corresponds to the ζ closes to 1/2, has proven to be localized (extended) in the localized (delocalized) phase. 28,29,49,50 Here, we show that all eigenvectors of EH has this property. To verify it numerically, we plot the U matrix composed of the EH eigenvectors for the PRBM model in Fig.…”