Thermal Entanglement in Disordered Spin Chains: Localization, Thresholds, and the Quantum-to-Classical Crossover

TL;DR

This paper explores how disorder and temperature influence thermal entanglement in spin chains, revealing phase-dependent thresholds and decay behaviors that shed light on the quantum-to-classical transition in many-body systems.

Contribution

It provides an analytical framework for understanding mixed-state entanglement in disordered spin chains and distinguishes entanglement behavior across localized and ergodic phases.

Findings

Entanglement vanishes above phase-dependent temperature thresholds.

Entanglement decays exponentially with spin separation.

Disorder and temperature critically affect entanglement in many-body systems.

Abstract

We investigate the mixed-state entanglement between two spins embedded in the XXZ Heisenberg chain under thermal equilibrium. By deriving an analytical expression for the entanglement of two-spin thermal states and extending this analysis to larger spin chains, we demonstrate that mixed-state entanglement is profoundly shaped by both disorder and temperature. Our results reveal a sharp distinction between many-body localized (MBL) and ergodic phases, with entanglement vanishing above different finite temperature thresholds. Furthermore, by analyzing non-adjacent spins, we uncover an approximate exponential decay of entanglement with separation. This work advances the understanding of the quantum-to-classical transition by linking the entanglement properties of small subsystems to the broader thermal environment, offering a explanation for the absence of entanglement in macroscopic systems. These findings provide critical insights into quantum many-body physics, bridging concepts from thermalization, localization, and quantum information theory.