Regular Article

Distribution of entanglement Hamiltonian spectrum in free fermion models

Department of Physics, Faculty of Basic Sciences, University of Mazandaran, P.O. Box 47416-95447, Babolsar, Iran

^a e-mail: mp11h@my.fsu.edu

Received: 27 January 2020
Received in final form: 9 March 2020
Published online: 22 June 2020

Abstract

We studied numerically the distribution of the entanglement Hamiltonian eigenvalues in two one-dimensional free fermion models and the typical three-dimensional Anderson model. We showed numerically that this distribution depends on the phase of the system: in the delocalized phase it is centered around very small values and in the localized phase, picks of the distribution goes to larger values. We therefore, based on the distribution of entanglement Hamiltonian eigenvalues, explain the behavior of the entanglement entropy in different phases. In addition we propose the smallest magnitude entanglement Hamiltonian eigenvalue as a characterization of phase and phase transition point (although it does not locate the phase transition point very sharply), and we verify it in the mentioned models.