Scalet proves a finite entanglement length for one-dimensional spin-chain Gibbs states at any finite temperature, so left and right half-chains become exactly separable once a long enough interval is traced out
Scalet proves that for any finite-range, bounded-strength local Hamiltonian on a one-dimensional spin chain at any fixed finite temperature, there exists an entanglement length ℓ depending only on temperature and locality, not on system size, such that whenever the middle interval B satisfies |B| ≥ ℓ, tracing out B from the tripartite Gibbs state ρABC yields a state ρAC that is separable between A and C; consequently entanglement of formation, distillable entanglement, entanglement cost, and entanglement relative entropy are exactly zero on that state, the statement holds uniformly in system size and extends to the KMS state of the infinite system, and the author calls this a spatial sudden death of entanglement.