Power-Law Entanglement Spectrum in Many-Body Localized Phases

TL;DR

This paper reveals that many-body localized phases exhibit power-law entanglement spectra due to local integrals of motion, providing a new way to distinguish these phases from ergodic and critical systems.

Contribution

It demonstrates that many-body localized systems have power-law entanglement spectra and introduces a matrix-product state algorithm for studying large systems near the localization transition.

Findings

Power-law entanglement spectra characterize many-body localized phases.

The spectra differ from those of ergodic and critical systems.

A new algorithm enables analysis of large systems near the localization transition.

Abstract

The entanglement spectrum of the reduced density matrix contains information beyond the von Neumann entropy and provides unique insights into exotic orders or critical behavior of quantum systems. Here, we show that strongly disordered systems in the many-body localized phase have power-law entanglement spectra, arising from the presence of extensively many local integrals of motion. The power-law entanglement spectrum distinguishes many-body localized systems from ergodic systems, as well as from ground states of gapped integrable models or free systems in the vicinity of scale-invariant critical points. We confirm our results using large-scale exact diagonalization. In addition, we develop a matrix-product state algorithm which allows us to access the eigenstates of large systems close to the localization transition, and discuss general implications of our results for variational studies of highly excited eigenstates in many-body localized systems.