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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
World Scientific Publishing
2011
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| Subjects: | |
| Online Access: | http://irep.iium.edu.my/6519/ http://irep.iium.edu.my/6519/ http://irep.iium.edu.my/6519/ http://irep.iium.edu.my/6519/1/acmfms-idaqp%282011%29.pdf |
| Summary: | 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
of QMC associated with such a model, this means the QMC does not depend on the
boundary conditions. |
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