Interplay between quantum phase transitions and the behavior of quantum correlations at finite temperatures

Abstract

We review the main results and ideas showing that quantum correlations at finite temperatures (T), in particular quantum discord, are useful tools in characterizing quantum phase transitions that only occur, in principle, at the unattainable absolute zero temperature. We first review some interesting results about the behavior of thermal quantum discord for small spin-1/2 chains and show that they already give us important hints of the infinite chain behavior. We then study in detail and in the thermodynamic limit (infinite chains) the thermal quantum correlations for the XXZ and XY models, where one can clearly appreciate that the behavior of thermal quantum discord at finite T is a useful tool to spotlight the critical point of a quantum phase transition.

v1: One column, 18 pages, 9 figures; submitted to Int. J. Mod. Phys. B, special issue "Classical Vs Quantum correlations in composite systems" edited by L. Amico, S. Bose, V. Korepin and V. Vedral; v2: published version

References in corpus (11)

• Necessary and sufficient condition for non-zero quantum discord
• Quantum Phase Transitions and Bipartite Entanglement
• Entanglement versus Correlations in Spin Systems
• Quantum discord and quantum phase transition in spin chains
• Quantum discord for general two--qubit states: Analytical progress
• Localizable Entanglement
• Multipartite Entanglement Signature of Quantum Phase Transitions
• Entanglement and Quantum Phase Transition Revisited
• Operational Classification and Quantification of Multipartite Entangled States
• Symmetry breaking effects upon bipartite and multipartite entanglement in the XY model
• Enhancement of pairwise entanglement from $\mathbbm{Z}_2$ symmetry breaking