Entanglement critical length at the many-body localization transition

Year: 2017

Authors: Pietracaprina F., Parisi G., Mariano A., Pascazio S., Scardicchio A.

Autors Affiliation: Univ Roma La Sapienza, Dipartimento Fis, I-00185 Rome, Italy;‎ Ist Nazl Fis Nucl, Sez Roma 1, CNR NANOTEC UOS Roma, I-00185 Rome, Italy; ENEA, Italian Natl Agcy New Technol Energy & Sustainabl, Viale Japigia 188, I-70126 Bari, Italy; Univ Bari, Dipartimento Fis, I-70126 Bari, Italy;‎ CNR, INO, I-50019 Sesto Fiorentino, Italy; Ist Nazl Fis Nucl, Sez Bari, I-70126 Bari, Italy; Abdus Salam Int Ctr Theoret Phys, Str Costiera 11, I-34151 Trieste, Italy; Ist Nazl Fis Nucl, Sez 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. From the analysis we extract a correlation length L-s(h) determining the minimum system size to enter the asymptotic region. We find that L-s(h) diverges at the MBL transition. We discuss the nature of the subleading corrections to the entanglement spectrum distribution and to the entanglement entropy.

Journal/Review: JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT

Volume: 2017      Pages from: 113102-1  to: 113102-13

KeyWords: entanglement entropies; many body localization
DOI: 10.1088/1742-5468/aa9338

Citations: 19
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