Exponential spatial decay of spin-spin correlations in translation invariant quasi-free states
Résumé
We study the spatial decay of the transversal spin-spin correlations in translation invariant quasi-free states on the canonical anticommutation relation algebra on the discrete line. We establish a simple criterion on the spectrum of the density of the quasi-free state which ensures the decay to be exponential. Moreover, we illustrate exponential and slower decay with the example of the XY spin chain out of equilibrium, in thermal equilibrium at positive temperature, in the ground state, and in the chaotic state