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Title: Nature and measure of entanglement in quantum phase transitions

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-(1/2) 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 inmore » 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.« less

Authors:
 [1]; ; ; ;  [1]
  1. Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
Publication Date:
OSTI Identifier:
20646347
Resource Type:
Journal Article
Journal Name:
Physical Review. A
Additional Journal Information:
Journal Volume: 70; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevA.70.042311; (c) 2004 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; ALGEBRA; ANISOTROPY; CORRELATIONS; ENERGY LEVELS; EXACT SOLUTIONS; FERMIONS; LIE GROUPS; MAGNETIC FIELDS; PHASE TRANSFORMATIONS; QUANTUM MECHANICS; SPIN; SYMMETRY BREAKING; TRANSFORMATIONS

Citation Formats

Somma, Rolando, Centro Atomico Bariloche and Instituto Balseiro, 8400 San Carlos de Bariloche, Ortiz, Gerardo, Barnum, Howard, Knill, Emanuel, and Viola, Lorenza. Nature and measure of entanglement in quantum phase transitions. United States: N. p., 2004. Web. doi:10.1103/PhysRevA.70.042311.
Somma, Rolando, Centro Atomico Bariloche and Instituto Balseiro, 8400 San Carlos de Bariloche, Ortiz, Gerardo, Barnum, Howard, Knill, Emanuel, & Viola, Lorenza. Nature and measure of entanglement in quantum phase transitions. United States. https://doi.org/10.1103/PhysRevA.70.042311
Somma, Rolando, Centro Atomico Bariloche and Instituto Balseiro, 8400 San Carlos de Bariloche, Ortiz, Gerardo, Barnum, Howard, Knill, Emanuel, and Viola, Lorenza. 2004. "Nature and measure of entanglement in quantum phase transitions". United States. https://doi.org/10.1103/PhysRevA.70.042311.
@article{osti_20646347,
title = {Nature and measure of entanglement in quantum phase transitions},
author = {Somma, Rolando and Centro Atomico Bariloche and Instituto Balseiro, 8400 San Carlos de Bariloche and Ortiz, Gerardo and Barnum, Howard and Knill, Emanuel and Viola, Lorenza},
abstractNote = {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-(1/2) 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.},
doi = {10.1103/PhysRevA.70.042311},
url = {https://www.osti.gov/biblio/20646347}, journal = {Physical Review. A},
issn = {1050-2947},
number = 4,
volume = 70,
place = {United States},
year = {Fri Oct 01 00:00:00 EDT 2004},
month = {Fri Oct 01 00:00:00 EDT 2004}
}