Clustering property for quantum Markov chains on the comb graph

Abdessatar Souissi; El Gheteb Soueidy; Mohamed Rhaima; Abdessatar Souissi; El Gheteb Soueidy; Mohamed Rhaima

doi:10.3934/math.2023396

AIMS Mathematics

2023, Volume 8, Issue 4: 7865-7880. doi: 10.3934/math.2023396

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Research article

Clustering property for quantum Markov chains on the comb graph

1.
Department of Management Information Systems, College of Business Management, Qassim University, ArRass, Saudi Arabia
2.
Department of Mathematics and Informatics, Faculty of Sciences and Technologies, University of Nouakchott, Nouakchott, Mauritania
3.
Department of Statistics and Operations Research, College of Sciences, King Saud University, P. O. Box, Riyadh 11451, Saudi Arabia
4.
Preparatory Institute for Scientific and Technical Studies, University of Carthage, Av. of the Republic, Carthage 1054, Tunisia

Received: 28 September 2022 Revised: 10 January 2023 Accepted: 14 January 2023 Published: 31 January 2023
MSC : 46L53, 46L60, 82B10, 81Q10

Quantum Markov chains (QMCs) on graphs and trees were investigated in connection with many important models arising from quantum statistical mechanics and quantum information. These quantum states generate many important properties such as quantum phase transition and clustering properties. In the present paper, we propose a construction of QMCs associated with an $ XX $-Ising model over the comb graph $ \mathbb N\rhd_0 \mathbb Z $. Mainly, we prove that the QMC associated with the disordered phase, enjoys a clustering property.
- quantum Markov chain,
- Ising model,
- comb graph,
- clustering property
Citation: Abdessatar Souissi, El Gheteb Soueidy, Mohamed Rhaima. Clustering property for quantum Markov chains on the comb graph[J]. AIMS Mathematics, 2023, 8(4): 7865-7880. doi: 10.3934/math.2023396

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Abstract

Quantum Markov chains (QMCs) on graphs and trees were investigated in connection with many important models arising from quantum statistical mechanics and quantum information. These quantum states generate many important properties such as quantum phase transition and clustering properties. In the present paper, we propose a construction of QMCs associated with an $ XX $-Ising model over the comb graph $ \mathbb N\rhd_0 \mathbb Z $. Mainly, we prove that the QMC associated with the disordered phase, enjoys a clustering property.

References

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