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 \(\bar X_\Lambda : = \frac{1}{{|\Lambda |}}\Sigma _{i \in \Lambda } X_i \), 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 \(\frac{1}{{|\Lambda |}}\Sigma _{i \in \Lambda } \delta _{X_i } \)

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Netočný, K., Redig, F. Large Deviations for Quantum Spin Systems. Journal of Statistical Physics 117, 521–547 (2004). https://doi.org/10.1007/s10955-004-3452-4

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  • Large deviation principle
  • central limit theorem
  • boundary terms
  • cluster expansion
  • Goldon–Thompson inequality