On the Algebra of Fluctuation in Quantum Spin Chains
Mathematical Physics
2015-06-26 v1 math.MP
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 -KMS condition if the microscopic state is a -KMS state.
Cite
@article{arxiv.math-ph/0202011,
title = {On the Algebra of Fluctuation in Quantum Spin Chains},
author = {Taku Matsui},
journal= {arXiv preprint arXiv:math-ph/0202011},
year = {2015}
}