Structure of quantum entanglement at a finite temperature critical point

Abstract

We introduce a framework to distinguish long-range quantum entanglement from long-range classical correlations close to a finite temperature critical point in a quantum system. In particular, we employ "tripartite entanglement negativity,"a mixed-state entanglement measure, to cancel out critical correlations that are purely classical in origin. As an application, we study an exactly solvable model, and find that the tripartite negativity does not exhibit any singularity in the thermodynamic limit across the transition. This indicates that the long-distance critical fluctuations are completely classical, and it allows one to define a "quantum correlation length"that remains finite at the transition despite a divergent physical correlation length. Motivated by our model, we also study mixed-state entanglement in tight-binding models of bosons with U(1) and time-reversal symmetries. By employing Glauber-Sudarshan representation, we find a surprising result that such states have zero entanglement.