On Quantum Markov Chains on Cayley tree I: uniqueness of the associated chain with XY-model on the Cayley tree of order two

Details On Quantum Markov Chains on Cayley tree I: uniqueness of the associated chain with XY-model on the Cayley tree of order two On Quantum Markov Chains on Cayley tree I: uniqueness of the associated chain with XY-model on the Cayley tree of order two

2010-04-21

arxiv.org/abs/1004.3623v2

Infinite Dim. Anal. Quantum Probab. Related Topics Vol. 14, No. 3 (2011) 443--463

Physics

Mathematical Physics

19 pages

Scientific paper

10.1142/S021902571100447X

In the present paper we study forward Quantum Markov Chains (QMC) defined on Cayley tree. A construction of such QMC is provided, namely we construct states on finite volumes with boundary conditions, and define QMC as a weak limit of those states which depends on the boundary conditions. Using the provided construction we investigate QMC associated with XY-model on a Caylay tree of order two. We prove uniqueness of QMC associated with such a model, this means the QMC does not depend on the boundary conditions.

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