Higher-dimensional quantum Gibbs correlation decay

The problem asks whether quantum Gibbs states on geometrically local systems in higher dimensions exhibit correlation decay throughout the zero-free regime, without requiring logarithmic separation between observables. No proposer or date is identified in the retrieved material.

Known results

• High-temperature quantum Gibbs states have clustering of conditional mutual information, with exponential decay for short-range interactions (2020).
• Exponential mutual-information decay is known for local Hamiltonians under high-temperature conditions (2022).
• Stronger correlation decay is proved in any dimension under a local-effective-Hamiltonian condition; commuting models provide an important case (2024).
• Decay-to-locality and stability results apply in any dimension, with explicit high-temperature exponential decay established for several short-range settings.

2026 zero-free-disk result

A recent paper on when quantum thermal states look classical establishes a zero-free disk and states exponential-decay and related Gibbs-state properties throughout that disk. The retrieved material does not verify that its theorem removes the logarithmic separation between observables in the exact higher-dimensional formulation, so it is relevant partial progress rather than a resolution.

Current status (as of March 2026): Related partial results are established, but the exact higher-dimensional zero-free-regime statement without logarithmic separation remains open.