Uniqueness of quantum Markov chains associated with an XY-model on a cayley tree of order 2

L. Accardi, F. M. Mukhamedov, M. Kh Saburov

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

We propose the construction of a quantum Markov chain that corresponds to a "forward" quantum Markov chain. In the given construction, the quantum Markov chain is defined as the limit of finite-dimensional states depending on the boundary conditions. A similar construction is widely used in the definition of Gibbs states in classical statistical mechanics. Using this construction, we study the quantum Markov chain associated with an XY-model on a Cayley tree. For this model, within the framework of the given construction, we prove the uniqueness of the quantum Markov chain, i. e., we show that the state is independent of the boundary conditions.

Original languageEnglish
Pages (from-to)162-174
Number of pages13
JournalMathematical Notes
Volume90
Issue number1
DOIs
Publication statusPublished - Aug 2011
Externally publishedYes

Keywords

  • Cayley tree
  • Gibbs state
  • XY-model
  • dynamical system
  • graph
  • phase transition
  • quantum Markov chain
  • quasiconditional expectation
  • quasilocal algebra

ASJC Scopus subject areas

  • General Mathematics

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