Abstract
In the present paper, we study forward quantum Markov chains (QMC) defined on a Cayley tree. Using the tree structure of graphs, we give a construction of quantum Markov chains on a Cayley tree. By means of such constructions we prove the existence of a phase transition for the XY-model on a Cayley tree of order three in QMC scheme. By the phase transition we mean the existence of two distinct QMC for the given family of interaction operators \({\{K_{\langle x,y\rangle}\}}\).
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Communicated by Petr Kulish.
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Accardi, L., Mukhamedov, F. & Saburov, M. On Quantum Markov Chains on Cayley Tree II: Phase Transitions for the Associated Chain with XY-Model on the Cayley Tree of Order Three. Ann. Henri Poincaré 12, 1109–1144 (2011). https://doi.org/10.1007/s00023-011-0107-2
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DOI: https://doi.org/10.1007/s00023-011-0107-2