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Recurrence of a class of quantum Markov chains on trees

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  • Barhoumi, Abdessatar
  • Souissi, Abdessatar

Abstract

The problem of recurrence for quantum Markov chains on trees (QMCT), is more subtle than for 1D quantum Markov chains (QMC); it involves infinitely many rays due to the exponential growth of ramifications on the Cayley trees and their relevant constraints. We study criteria for recurrence of QMCT based on the correlations functions and boundary conditions. These represent a bridge between recurrence and phase transitions. Furthermore, we illustrate our results through an Ising model with competing interactions.

Suggested Citation

  • Barhoumi, Abdessatar & Souissi, Abdessatar, 2022. "Recurrence of a class of quantum Markov chains on trees," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008232
    DOI: 10.1016/j.chaos.2022.112644
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    Cited by:

    1. Souissi, Abdessatar & Soueidy, El Gheteb & Barhoumi, Abdessatar, 2023. "On a ψ-Mixing property for Entangled Markov Chains," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 613(C).

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