Universality of the negativity in the Lipkin-Meshkov-Glick model

Details Universality of the negativity in the Lipkin-Meshkov-Glick model Universality of the negativity in the Lipkin-Meshkov-Glick model

2009-10-06

arxiv.org/abs/0910.1011v2

Phys. Rev. A 81, 032311 (2010)

Physics

Condensed Matter

Statistical Mechanics

5 pages, 2 figures, published version

Scientific paper

10.1103/PhysRevA.81.032311

The entanglement between noncomplementary blocks of a many-body system, where a part of the system forms an ignored environment, is a largely untouched problem without analytic results. We rectify this gap by studying the logarithmic negativity between two macroscopic sets of spins in an arbitrary tripartition of a collection of mutually interacting spins described by the Lipkin-Meshkov-Glick Hamiltonian. This entanglement measure is found to be finite and universal at the critical point for any tripartition whereas it diverges for a bipartition. In this limiting case, we show that it behaves as the entanglement entropy, suggesting a deep relation between the scaling exponents of these two independently defined quantities which may be valid for other systems.

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