Nature and measure of entanglement in quantum phase transitions

Rolando Somma, Gerardo Ortiz, Howard Barnum, Emanuel Knill, and Lorenza Viola
Phys. Rev. A 70, 042311 – Published 18 October 2004

Abstract

Characterizing and quantifying quantum correlations in states of many-particle systems is at the core of a full understanding of phase transitions in matter. In this work, we continue our investigation of the notion of generalized entanglement [Barnum et al., Phys. Rev. A 68, 032308 (2003)] by focusing on a simple Lie-algebraic measure of purity of a quantum state relative to an observable set. For the algebra of local observables on multi-qubit systems, the resulting local purity measure is equivalent to a recently introduced global entanglement measure [Meyer and Wallach, J. Math. Phys. 43, 4273 (2002)]. In the condensed-matter setting, the notion of Lie-algebraic purity is exploited to identify and characterize the quantum phase transitions present in two exactly solvable models, namely the Lipkin-Meshkov-Glick model and the spin-12 anisotropic XY model in a transverse magnetic field. For the latter, we argue that a natural fermionic observable set arising after the Jordan-Wigner transformation better characterizes the transition than alternative measures based on qubits. This illustrates the usefulness of going beyond the standard subsystem-based framework while providing a global disorder parameter for this model. Our results show how generalized entanglement leads to useful tools for distinguishing between the ordered and disordered phases in the case of broken symmetry quantum phase transitions. Additional implications and possible extensions of concepts to other systems of interest in condensed-matter physics are also discussed.

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  • Received 12 March 2004

DOI:https://doi.org/10.1103/PhysRevA.70.042311

©2004 American Physical Society

Authors & Affiliations

Rolando Somma1,2,*, Gerardo Ortiz1, Howard Barnum1, Emanuel Knill1,†, and Lorenza Viola1,‡

  • 1Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
  • 2Centro Atómico Bariloche and Instituto Balseiro, 8400 San Carlos de Bariloche, Argentina

  • *Corresponding author. Email address: somma@lanl.gov
  • Present address: National Institute of Standards and Technology, Boulder, CO 80305, USA.
  • Present address: Department of Physics and Astronomy, Dartmouth College, Hanover, NH 03755, USA.

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Vol. 70, Iss. 4 — October 2004

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