On Translation Invariant Quantum Markov Chains associated with Ising-XY models on a Cayley tree

Farrukh Mukhamedov, Abdessatar Barhoumi, Abdessatar Souissi, Soueidy El Gheteb

Research output: Contribution to journalConference articlepeer-review

Abstract

In this paper, we consider the Ising-XY model with competing interactions on the Cayley tree of order two. This model can be seen as a non-commutative (i.e. J-XY -interactions on next-neighbor vertices) perturbation of the classical Ising model on the Cayley tree. For the considered model we establish the existence of three translation-invariant quantum Markov chains. We notice that if the XY -interactions vanish, i.e. J = 0, then one gets the Ising model. If the classical Ising model vanishes in the considered model, then we obtain XY -model for which it turns out there exists only one translation invariant QMC.

Original languageEnglish
Article number012006
JournalJournal of Physics: Conference Series
Volume819
Issue number1
DOIs
Publication statusPublished - Apr 3 2017
Event37th International Conference on Quantum Probability and Related Topics, QP 2016 - Kuantan, Malaysia
Duration: Aug 22 2016Aug 26 2016

ASJC Scopus subject areas

  • General Physics and Astronomy

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