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Annales Henri Poincaré

, Volume 4, Issue 1, pp 63–83 | Cite as

On the Algebra of Fluctuation in Quantum Spin Chains

  • T. Matsui
Original article

Abstract.

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.

Keywords

Time Evolution Limit Theorem Central Limit Central Limit Theorem Spin Chain 

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Copyright information

© Birkhäuser Verlag Basel, 2003

Authors and Affiliations

  • T. Matsui
    • 1
  1. 1.Graduate School of Mathematics, Kyushu University, 1-10-6 Hakozaki, Fukuoka 812-8581, Japan, e-mail: matsui@math.kyushu-u.ac.jpJapan

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