Refinement of quantum Markov states on trees. (20th August 2021)

• Record Type: Journal Article
• Authors: Mukhamedov, Farrukh; Souissi, Abdessatar
• Is Part Of: Journal of statistical mechanics. (2021:Aug.)
• Publication Date: 2021-08-20
• Subjects: correlation functions -- quantum phase transitions -- random graphs, networks -- solvable lattice models; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/ac150b
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: In the present paper, we propose a refinement for the notion of quantum Markov states (QMS) on trees. A structure theorem for QMS on general trees is proved. We notice that any restriction of QMS in the sense of reference Accardi and Fidaleo (2003 J. Funct. Anal. 200 324–347) is not necessarily to be a QMS. It turns out that localized QMS has the mentioned property which is called sub-Markov states, this allows us to characterize translation invariant QMS on regular trees.