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arXiv · 1004.3623

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

Luigi Accardi·Farrukh Mukhamedov·Mansoor Saburov
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Abstract

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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Luigi Accardi, Farrukh Mukhamedov, Mansoor Saburov. 2010-10-18. On Quantum Markov Chains on Cayley tree I: uniqueness of the associated chain with XY-model on the Cayley tree of order two. https://doi.org/10.1142/s021902571100447x

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