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

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.

preprint2010arXivOpen access
Luigi AccardiFarrukh MukhamedovMansoor Saburov
math-phmath.DSmath.FAmath.MP
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Luigi AccardiFarrukh MukhamedovMansoor Saburov

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