Structure of Quantum Entanglement at a Finite Temperature Critical Point

We propose a scheme to characterize long-range quantum entanglement close to a finite temperature critical point using tripartite entanglement negativity. Across a conventional order-disorder transition, tripartite negativity does not exhibit any singularity in the thermodynamic limit, in contrast to the short-range component of negativity, which is singular. This indicates that the long-distance critical fluctuations are completely classical, allowing one to define a ‘quantum correlation length’ that remains finite at the transition despite a divergent physical correlation length.