Strong decay of correlations for Gibbs states in any dimension

Understand

Quantum systems in thermal equilibrium are described using Gibbs states.

• The correlations in such states determine how difficult it is to describe or simulate them.
• In this article, we show that if the Gibbs state of a quantum system satisfies that each of its marginals admits a local effective Hamiltonian with short-range interactions, then it satisfies a mixing condition, that is, for any regions $A$, $C$ the distance of the reduced state $\rho_{AC}$ on these regions to the product of its marginals, $$\| \rho_{AC} \rho_A^{-1} \otimes \rho_C^{-1} - 1_{AC}\|\, ,$$ decays exponentially with the distance between regions $A$ and $C$.
• This mixing condition is stronger than other commonly studied measures of correlation.