Abstract
Abstract: We construct quantum Markov chains (QMCs) over comb graphs. As an application of this construction, we prove the existence of a disordered phase for Ising type models (within the QMC scheme) over comb graphs. Moreover, we also establish that the associated QMC has the clustering property with respect to translations of the graph. We stress that this paper is the first one where a nontrivial example of QMCs over irregular graphs is given.
Original language | English |
---|---|
Pages (from-to) | 178-192 |
Number of pages | 15 |
Journal | Proceedings of the Steklov Institute of Mathematics |
Volume | 313 |
Issue number | 1 |
DOIs | |
Publication status | Published - Jul 2021 |
Keywords
- clustering
- comb graph
- Ising model
- quantum Markov chain
ASJC Scopus subject areas
- Mathematics (miscellaneous)