Entanglement transitions as a probe of quasiparticles and quantum thermalization

TL;DR

This paper proposes a new diagnostic based on entanglement negativity to distinguish different quantum thermalization behaviors and phases, revealing sharp transitions and characteristic scalings in various many-body systems.

Contribution

It introduces a novel entanglement negativity-based diagnostic for quantum thermalization and provides analytical bounds, supported by numerical evidence, to classify phases like thermalizing, quasiparticle, and localized systems.

Findings

Negativity exhibits a sharp transition from area-law to volume-law scaling in self-thermalizing systems.

Quasiparticle systems show volume-law negativity regardless of subsystem size.

Many-body localized systems display area-law negativity in eigenstates and volume-law after long-time evolution.

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.