Quantum entanglement in thermal states is expected to decay with distance. The question is how: gradually, asymptotically approaching zero but never reaching it, or sharply, vanishing entirely beyond some finite range?
Bakshi and colleagues (arXiv:2602.20694) prove a finite entanglement length for the Gibbs state of any local Hamiltonian on a spin chain at any finite temperature. Remove an interval of size equal to or greater than this entanglement length, and the remaining left and right half-chains are in a separable state — not approximately separable, not weakly entangled, but exactly separable. Zero entanglement. The quantum correlations undergo sudden death at a finite distance.
This holds at any finite temperature. Not just high temperature, where thermal fluctuations are expected to dominate quantum correlations. Any finite temperature. The entanglement length depends on the temperature and the Hamiltonian, but its finiteness does not. There is always a distance beyond which the thermal state has no entanglement whatsoever.
The result is stronger than exponential decay of correlations, which is already known for thermal states. Exponential decay says correlations become small. Separability says entanglement is exactly zero. Small correlations can still be entangled — the distinction between classical and quantum correlations is not about magnitude. A state can have exponentially small but nonzero entanglement. This result shows that for thermal spin chains, even that residual entanglement disappears beyond a finite range.
The general observation: a quantity that decays continuously in magnitude may still have a sharp boundary in kind. The transition from entangled to separable is qualitative, not quantitative — and that qualitative transition happens at a finite distance, not asymptotically. The smooth decay of correlations masks a sharp structural change in their character.