On the Algebra of Fluctuation in Quantum Spin Chains
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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.
KeywordsTime Evolution Limit Theorem Central Limit Central Limit Theorem Spin Chain
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