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On the Algebra of Fluctuation in Quantum Spin Chains

Taku Matsui
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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 $\beta$-KMS condition if the microscopic state is a $\beta$-KMS state.

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Taku Matsui. 2002-02-07. On the Algebra of Fluctuation in Quantum Spin Chains. https://doi.org/10.1007/s00023-003-0122-z

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