Local Measures of Entanglement and Critical Exponents at Quantum Phase Transitions

Details Local Measures of Entanglement and Critical Exponents at Quantum Phase Transitions Local Measures of Entanglement and Critical Exponents at Quantum Phase Transitions

2005-08-31

arxiv.org/abs/quant-ph/0508236v4

Phys. Rev. A 73, 010303(R) (2006)

Physics

Quantum Physics

5 pages, 2 eps figures. Abstract replaced, minor changes in the text

Scientific paper

10.1103/PhysRevA.73.010303

We discuss on general grounds some local indicators of entanglement, that have been proposed recently for the study and classification of quantum phase transitions. In particular, we focus on the capability of entanglement in detecting quantum critical points and related exponents. We show that the singularities observed in all local measures of entanglement are a consequence of the scaling hypothesis. In particular, as every non-trivial local observable is expected to be singular at criticality, we single out the most relevant one (in the renormalization group sense) as the best-suited for finite-size scaling analysis. The proposed method is checked on a couple of one-dimensional spin systems. The present analysis shows that the singular behaviour of local measures of entanglement is fully encompassed in the usual statistical mechanics framework.

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