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Phys. Rev. A 71, 062324 (2005) [14 pages]

Entanglement across a transition to quantum chaos

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Carlos Mejía-Monasterio1,*, Guliano Benenti1,2,3,†, Gabriel G. Carlo1,2,‡, and Giulio Casati1,2,3,§
1Center for Nonlinear and Complex Systems, Università degli Studi dell’Insubria, via Vallegio 11, Como 22100, Italy
2Istituto Nazionale per la Fisica della Materia, Unità di Como, via Vallegio 11, Como 22100, Italy
3Istituto Nazionale di Fisica Nucleare, Sezione di Milano, Via Celoria 16, 20133 Milano, Italy

Received 29 October 2004; revised 10 February 2005; published 20 June 2005

We study the relation between entanglement and quantum chaos in one- and two-dimensional spin-1∕2 lattice models, which exhibit mixing of the noninteracting eigenfunctions and transition from integrability to quantum chaos. Contrary to what occurs in a quantum phase transition, the onset of quantum chaos is not a property of the ground state but takes place for any typical many-spin quantum state. We study bipartite and pairwise entanglement measures—namely, the reduced von Neumann entropy and the concurrence—and discuss quantum entanglement sharing. Our results suggest that the behavior of the entanglement is related to the mixing of the eigenfunctions rather than to the transition to chaos.

© 2005 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevA.71.062324
DOI:
10.1103/PhysRevA.71.062324
PACS:
03.67.Lx, 05.45.Pq, 05.45.Mt, 24.10.Cn

*Electronic address: carlos.mejia@uninsubria.it; URL http:∕∕scienze-como.uninsubria.it∕complexcomo

†Electronic address: giuliano.benenti@uninsubria.it

‡Electronic address: gabriel.carlo@uninsubria.it

§Electronic address: giulio.casati@uninsubria.it

 
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