TY - JOUR

T1 - A quantum Markov chain approach to phase transitions for quantum Ising model with competing XY -interactions on a Cayley tree

AU - Mukhamedov, Farrukh

AU - Barhoumi, Abdessatar

AU - Souissi, Abdessatar

AU - El Gheteb, Soueidy

N1 - Publisher Copyright:
© 2020 Author(s).

PY - 2020/9/1

Y1 - 2020/9/1

N2 - The main aim of the present paper by means of the quantum Markov chain (QMC) approach is to establish the existence of a phase transition for the quantum Ising model with competing XY interaction. In this scheme, the C*-algebraic approach is employed to the phase transition problem. Note that these kinds of models do not have one-dimensional analogs, i.e., the considered model persists only on trees. It turns out that if the Ising part interactions vanish, then the model with only competing XY-interactions on the Cayley tree of order two does not have a phase transition. By phase transition, we mean the existence of two distinct QMCs that are not quasi-equivalent and their supports do not overlap. Moreover, it is also shown that the QMC associated with the model has a clustering property, which implies that the von Neumann algebras corresponding to the states are factors.

AB - The main aim of the present paper by means of the quantum Markov chain (QMC) approach is to establish the existence of a phase transition for the quantum Ising model with competing XY interaction. In this scheme, the C*-algebraic approach is employed to the phase transition problem. Note that these kinds of models do not have one-dimensional analogs, i.e., the considered model persists only on trees. It turns out that if the Ising part interactions vanish, then the model with only competing XY-interactions on the Cayley tree of order two does not have a phase transition. By phase transition, we mean the existence of two distinct QMCs that are not quasi-equivalent and their supports do not overlap. Moreover, it is also shown that the QMC associated with the model has a clustering property, which implies that the von Neumann algebras corresponding to the states are factors.

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U2 - 10.1063/5.0004889

DO - 10.1063/5.0004889

M3 - Article

AN - SCOPUS:85092604443

SN - 0022-2488

VL - 61

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 9

M1 - 093505

ER -