Entanglement transitions as a probe of quasiparticles and quantum thermalization

Abstract

We introduce a diagnostic for quantum thermalization based on mixed-state entanglement. Specifically, given a pure state on a tripartite system $ABC$, we study the scaling of entanglement negativity between $A$ and $B$. For representative states of self-thermalizing systems, either eigenstates or states obtained by a long-time evolution of product states, negativity shows a sharp transition from an area-law scaling to a volume-law scaling when the subsystem volume fraction is tuned across a finite critical value. In contrast, for a system with quasiparticles, it exhibits a volume-law scaling irrespective of the subsystem fraction. For many-body localized systems, the same quantity shows an area-law scaling for eigenstates, and volume-law scaling for long-time evolved product states, irrespective of the subsystem fraction. We provide a combination of numerical observations and analytical arguments in support of our conjecture. Along the way, we prove and utilize a `continuity bound' for negativity: we bound the difference in negativity for two density matrices in terms of the Hilbert-Schmidt norm of their difference.