On the algebra of fluctuation in quantum spin chains

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17 Citations (Scopus)


We present a proof of the central limit theorem for a pair of mutually non-commuting operators in mixing quantum spin chains. The operators are not necessarily strictly local but quasi-local. As a corollary we obtain a direct construction of the time evolution of the algebra of normal fluctuation for Gibbs states of finite range interactions on a one-dimensional lattice. We show that the state of the algebra of normal fluctuation satisfies the β-KMS condition if the microscopic state is a β-KMS state. We show that any mixing finitely correlated state satisfies our assumption for the central limit theorem.

Original languageEnglish
Pages (from-to)63-83
Number of pages21
JournalAnnales Henri Poincare
Issue number1
Publication statusPublished - 2003

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics


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