Taku Matsui
On the Algebra of
Fluctuation in Quantum Spin Chains.
(53K, latex)
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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We show that any mixing finitely correlated state satisfies
our assumption for the central limit theorem.