Spatial Entanglement Sudden Death in Spin Chains at All Temperatures

TL;DR

This paper proves that in spin chains at any finite temperature, entanglement is confined within a finite length, beyond which the system becomes separable, highlighting a fundamental limit on quantum correlations in thermal states.

Contribution

It establishes a universal finite entanglement length for Gibbs states of local Hamiltonians at all temperatures, demonstrating entanglement's spatial decay in thermal equilibrium.

Findings

Entanglement length is finite at all temperatures.

Removing a segment of size equal to the entanglement length renders the halves separable.

Quantum correlations are spatially limited in thermal spin chains.

Abstract

We prove a finite entanglement length for the Gibbs state of any local Hamiltonian on a spin chain at any finite temperature: After removing an interval of size at least equal to the entanglement length, the remaining left and right half-chains are in a separable state.