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Lieb and Robinson: a finite propagation-velocity bound for quantum spin systems

Contribution grade

Quantum many-body mathematical physics · Exact theorem and reusable mathematical method

Reference score250,000Provisional editorial estimate of this exact contribution; its grade is assessed separately.

What changed

For translation-invariant finite-range interactions on a quantum spin lattice with finite-dimensional site spaces, the norm of a commutator between separated local observables becomes exponentially small outside a sufficiently fast space-time cone. The proof bounds dynamical influence independently of the chosen quantum state.

Scientific scope

For translation-invariant finite-range interactions on a quantum spin lattice with finite-dimensional site spaces, the norm of a commutator between separated local observables becomes exponentially small outside a sufficiently fast space-time cone. The proof bounds dynamical influence independently of the chosen quantum state. This is an exponentially suppressed tail, not exact relativistic causality or a theorem for arbitrary long-range and unbounded interactions. The finite velocity bound need not be sharp. The paper remarks on exponentially decaying extensions, but the core staged claim uses its explicit finite-range hypotheses.

Evidence

The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. This is an exponentially suppressed tail, not exact relativistic causality or a theorem for arbitrary long-range and unbounded interactions. The finite velocity bound need not be sharp. The paper remarks on exponentially decaying extensions, but the core staged claim uses its explicit finite-range hypotheses.

Contributors

Provisional WRS assessment, edition 2026-10-23.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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