Correlations and coherence are distinctive features of quantum many-body states. When considering quantum ground states, they are essentially synonymous -- quantum correlations manifest the existence of coherent quantum fluctuations in the system, and are the necessary condition for the existence of entanglement between any two subsystems. But, when moving to mixed states, the situation becomes blurred, as correlations acquire also a classical, incoherent nature, and entanglement is no longer unambiguously quantified.
In this seminar I will introduce a general separation scheme between quantum/coherent correlations and thermal/incoherence correlations for mixed states, which is deeply motivated by the equilibrium statistical mechanics of quantum many-body systems. Quantum correlations are associated with the violation of a classical fluctuation-response identity, invoking the full structure of the imaginary-time propagator, and lending themselves to a direct experimental measure. The existence of quantum correlations among two subsystems A and B negates a physically motivated form of separability (namely of absence of entanglement), in which correlations are generated by a hidden classical source. Most strikingly, two-point quantum correlations in extended quantum systems are numerically found to decay exponentially at any finite temperature, exhibiting a novel quantum coherence length which is completely independent of the ordinary correlation length. This new length is found to be a very sensitive probe of the quantum critical fan of systems exhibiting a quantum phase transition.