Two-component Structure in the Entanglement Spectrum of Highly Excited States

TL;DR

This paper reveals a universal two-component structure in the entanglement spectrum of highly excited states in models with many-body localization, linking the spectrum's universal part to random matrix theory and its nonuniversal part to model-specific deviations.

Contribution

It introduces the concept of a two-component entanglement spectrum structure and proposes a new order parameter for the many-body localization transition.

Findings

Universal part fraction decreases near the critical point.

Nonuniversal part reflects deviations from true randomness.

Structure observed in toy models as well.

Abstract

We study the entanglement spectrum of highly excited eigenstates of two known models that exhibit a many-body localization transition, namely the one-dimensional random-field Heisenberg model and the quantum random energy model. Our results indicate that the entanglement spectrum shows a "two-component" structure: a universal part that is associated with random matrix theory, and a nonuniversal part that is model dependent. The non-universal part manifests the deviation of the highly excited eigenstate from a true random state even in the thermalized phase where the eigenstate thermalization hypothesis holds. The fraction of the spectrum containing the universal part decreases as one approaches the critical point and vanishes in the localized phase in the thermodynamic limit. We use the universal part fraction to construct an order parameter for measuring the degree of randomness of a generic highly excited state, which is also a promising candidate for studying the many-body localization transition. Two toy models based on Rokhsar-Kivelson type wave functions are constructed and their entanglement spectra are shown to exhibit the same structure.