Classical Correlation and Quantum Discord in Critical Systems

Details Classical Correlation and Quantum Discord in Critical Systems Classical Correlation and Quantum Discord in Critical Systems

2009-05-08

arxiv.org/abs/0905.1347v3

Phys. Rev. A 80, 022108 (2009)

Physics

Quantum Physics

10 pages, 8 figures. v3: minor changes. Published version. v2: conclusion section improved, references updated, and minor corr

Scientific paper

We discuss the behavior of quantum and classical pairwise correlations in critical systems, with the quantumness of the correlations measured by the quantum discord. We analytically derive these correlations for general real density matrices displaying $Z_2$ symmetry. As an illustration, we analyze both the XXZ and the transverse field Ising models. Finite-size as well as infinite chains are investigated and the quantum criticality is discussed. Moreover, we identify the spin functions that govern the correlations. As a further example, we also consider correlations in the Hartree-Fock ground state of the Lipkin-Meshkov-Glick model. It is then shown that both classical correlation and quantum discord exhibit signatures of the quantum phase transitions.

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