title: Power-Law Entanglement Spectrum in Many-Body Localized Phases.
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.
authors: Department of Physics, University of California, Berkeley, California 94720, USA.
authors: Maksym
authors: M
authors: Serbyn
authors: School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, United Kingdom.
authors: Alexios A
authors: AA
authors: Michailidis
authors: Department of Theoretical Physics, University of Geneva, 24 quai Ernest-Ansermet, 1211 Geneva, Switzerland.
authors: Dmitry A
authors: DA
authors: Abanin
authors: School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT, United Kingdom.
authors: Z
authors: Z
authors: Papić