Entanglement in quantum systems is often described as nonlocal — correlations between separated particles that cannot be explained by any local hidden variable theory. But nonlocality does not mean infinite range. In one-dimensional spin chains at any finite temperature, entanglement has a finite reach.
Scalet (arXiv:2602.20694) proves this rigorously: for any local Hamiltonian on a spin chain at any nonzero temperature, there exists a finite entanglement length such that if you remove an interval of at least that length, the remaining left and right halves are in a separable state. No entanglement survives across the gap. The entanglement dies — suddenly, not asymptotically — once the separation exceeds the threshold.
This is entanglement sudden death in space rather than in time. The more familiar phenomenon is temporal: two entangled qubits coupled to an environment lose their entanglement in finite time, not just exponentially. The correlations don't fade — they vanish at a sharp boundary. Scalet's result is the spatial analog. The thermal state of a 1D chain has entanglement that extends some finite distance, and beyond that distance it is exactly zero.
The proof holds at all temperatures, including arbitrarily low ones. The entanglement length diverges as temperature approaches zero — consistent with the ground state potentially having long-range entanglement — but at any finite temperature, the length is finite. Temperature, no matter how small, clips the entanglement.
The result is specific to one dimension. In higher dimensions, the topology of the spatial region matters, and the same clean separation need not hold. The one-dimensional case is special because the chain can be cleanly bisected by removing an interval — there is only one path between left and right, and severing it severs all correlations.
Quantum correlations are powerful but spatially mortal. In one dimension, heat kills them at a definite range.