FisMat2017 - Submission - View

Abstract's title: Entanglement and length scales in a many body localizable system
Submitting author: Francesca Pietracaprina
Affiliation: Sapienza Università di Roma
Affiliation Address: Dipartimento di Fisica, Sapienza Università di Roma Piazzale Aldo Moro 5, 00185 Roma
Country: Italy
Oral presentation/Poster (Author's request): Oral presentation
Other authors and affiliations: Giorgio Parisi (1,2), Angelo Mariano (3), Saverio Pascazio (4,5,6), Antonello Scardicchio (7,8) (1) Dipartimento di Fisica, Universit\`a degli Studi di Roma ``La Sapienza'', I-00185, Roma, Italy (2) INFN, Sezione di Roma I, CNR-NANOTEC UOS Roma, I-00185, Roma, Italy (3) ENEA, Italian National Agency for New Technologies, Energy and Sustainable Economic Development, viale Japigia 188, I-70126, Bari, Italy (4) Dipartimento di Fisica, Universit\`{a} di Bari, I-70126 Bari, Italy (5) INO-CNR, 50019 Sesto Fiorentino, Italy (6) INFN, Sezione di Bari, I-70126 Bari, Italy (7) The Abdus Salam ICTP, Strada Costiera 11, I-34151 Trieste, Italy (8) INFN Sezione di Trieste, Via Valerio 2, I-34127 Trieste, Italy
Abstract

We study the details of the distribution of the entanglement spectrum (eigenvalues of the reduced density matrix) of a disordered spin chain exhibiting a many-body localization (MBL) transition. In the thermalizing region we identify the evolution under increasing system size of the eigenvalue distribution function, whose thermodynamic limit is close to (but possibly different from) the Marchenko-Pastur distribution. The aim of this talk is to show that deviations from Marchenko-Pastur of the probability distribution of the entanglement spectrum in the ergodic phase provide an important characterization of the ergodic phase of such a disordered system. Moreover, such deviations from Marchenko-Pastur can be used to define a correlation length $L_s(h)$, which determines the minimum system size to enter the asymptotic region and diverges at the MBL transition, and to predict the location and finite-size scaling exponents of the MBL transition. Finally, we discuss the nature of the subleading corrections to the entanglement spectrum distribution and to the entanglement entropy.
We show that the entanglement spectrum therefore appears to be a crucial quantity, being able to identify even the most subtle correlations that are present in the ergodic phase of a disordered quantum system.