Phase transitions and metastability in the distribution of the bipartite entanglement of a large quantum system

A. De Pasquale, P. Facchi, G. Parisi, S. Pascazio, and A. Scardicchio
Phys. Rev. A 81, 052324 – Published 19 May 2010

Abstract

We study the distribution of the Schmidt coefficients of the reduced density matrix of a quantum system in a pure state. By applying general methods of statistical mechanics, we introduce a fictitious temperature and a partition function and translate the problem in terms of the distribution of the eigenvalues of random matrices. We investigate the appearance of two phase transitions, one at a positive temperature, associated with very entangled states, and one at a negative temperature, signaling the appearance of a significant factorization in the many-body wave function. We also focus on the presence of metastable states (related to two-dimensional quantum gravity) and study the finite size corrections to the saddle point solution.

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  • Received 13 January 2010

DOI:https://doi.org/10.1103/PhysRevA.81.052324

©2010 American Physical Society

Authors & Affiliations

A. De Pasquale1,2,3, P. Facchi2,4, G. Parisi5,6, S. Pascazio1,2, and A. Scardicchio7,8

  • 1Dipartimento di Fisica, Università di Bari, I-70126 Bari, Italy
  • 2INFN, Sezione di Bari, I-70126 Bari, Italy
  • 3MECENAS, Università Federico II di Napoli, Via Mezzocannone 8, I-80134 Napoli, Italy
  • 4Dipartimento di Matematica, Università di Bari, I-70125 Bari, Italy
  • 5Dipartimento di Fisica, Università di Roma “La Sapienza”, Piazzale Aldo Moro 2, I-00185 Roma, Italy
  • 6Centre for Statistical Mechanics and Complexity (SMC), CNR-INFM, I-00185 Roma, Italy INFN Sezione di Roma, I-00185 Roma, Italy
  • 7Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, I-34014 Trieste, Italy
  • 8INFN, Sezione di Trieste, I-34014 Trieste, Italy

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Issue

Vol. 81, Iss. 5 — May 2010

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