title: Two-Component Structure in the Entanglement Spectrum of Highly Excited States.
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.
authors.affiliation: Physics Department, Boston University, Boston, Massachusetts 02215, USA.
authors.forename: Zhi-Cheng
authors.initials: ZC
authors.lastname: Yang
authors.affiliation: Physics Department, Boston University, Boston, Massachusetts 02215, USA.
authors.forename: Claudio
authors.initials: C
authors.lastname: Chamon
authors.affiliation: Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, People's Republic of China.
authors.forename: Alioscia
authors.initials: A
authors.lastname: Hamma
authors.affiliation: Department of Physics, University of Central Florida, Orlando, Florida 32816, USA.
authors.forename: Eduardo R
authors.initials: ER
authors.lastname: Mucciolo