Nature and Measure of Entanglement in Quantum Phase Transitions

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  • 4 March 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 turns out to be essentially 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 integrable models, namely the Lipkin-Meshkov-Glick model and the spin-1/2 anisotropic XY model in a transverse magnetic field. 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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