Large deviations for quantum spin systems

Abstract

We consider high temperature KMS states for quantum spin systems on a lattice. We prove a large deviation principle for the distribution of empirical averages $\frac{1}{|\Lambda |}{\sum }_{i\in \Lambda }{X}_i$, where the $X_i$'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 $\frac{1}{|\Lambda |}{\sum }_{i\in \Lambda }{\delta }_{X_i}$.

22 pages