Distribution of entanglement Hamiltonian spectrum in free fermion models

TL;DR

This paper investigates how the distribution of entanglement Hamiltonian eigenvalues varies across different phases in free fermion and Anderson models, linking it to entanglement entropy behavior and proposing a phase characterization method.

Contribution

It numerically analyzes entanglement Hamiltonian spectra in free fermion and Anderson models, revealing phase-dependent distribution patterns and proposing a new phase characterization metric.

Findings

Distribution centers around small values in delocalized phase

Distribution shifts to larger values in localized phase

Smallest eigenvalue can indicate phase and transition points

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.