Large Deviations for Quantum Spin Systems

AbstractWe consider high temperature KMS states for quantum spin systems on a lattice. We prove a large deviation principle for the distribution of empirical averages $$\bar X_\Lambda : = \frac{1}{{|\Lambda |}}\Sigma _{i \in \Lambda } X_i $$ , where the Xi's are copies of a self-adjoint element X (level one large deviations). From the analyticity of the generating function, we obtain the central limit theorem. We generalize to a level two large deviation principle for the distribution of $$\frac{1}{{|\Lambda |}}\Sigma _{i \in \Lambda } \delta _{X_i } $$