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Large deviations for quantum spin systems

K. Netocny·F. Redig
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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 $\frac{1}{|Λ|} \sum_{i\inΛ} X_i$, 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 $\frac{1}{|Λ|}\sum_{i\inΛ} δ_{X_i}$.

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K. Netocny, F. Redig. 2004-04-06. Large deviations for quantum spin systems. https://doi.org/10.1007/s10955-004-3452-4

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