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

Physical Review Letters
Zhi-Cheng YangEduardo R Mucciolo

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 nonuniversal 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.

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Citations

Dec 2, 2017·Scientific Reports·Bing-Tian YeHeng Fan
Dec 30, 2017·Physical Review Letters·Lev Vidmar, Marcos Rigol
Aug 31, 2018·Journal of Physics. Condensed Matter : an Institute of Physics Journal·Wen-Jia Rao
Jun 23, 2020·Journal of Physics. Condensed Matter : an Institute of Physics Journal·Rubah KausarXin Wan
Feb 23, 2020·Physical Review Letters·S C MorampudiC R Laumann
Oct 30, 2016·Physical Review Letters·Maksym SerbynZ Papić
Jan 5, 2019·Physical Review Letters·Yi-Ting HsuS Das Sarma
Nov 26, 2019·Physical Review Letters·Po-Yao ChangJ H Pixley
Jan 23, 2020·Physical Review. E·Tyler LeBlondMarcos Rigol
Nov 17, 2020·Physical Review Letters·Patrycja ŁydżbaLev Vidmar
Dec 18, 2020·Physical Review. E·Sanku Paul, Arnd Bäcker

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