TY - JOUR
T1 - Refinement of quantum Markov states on trees
AU - Mukhamedov, Farrukh
AU - Souissi, Abdessatar
N1 - Funding Information:
The authors gratefully acknowledge Qassim University, represented by the Deanship of Scientific Research, on the financial support for this research under the Number (10173-cba-2020-1-3-I) during the academic year 1442 AH/2020 AD.
Publisher Copyright:
© 2021 IOP Publishing Ltd and SISSA Medialab srl.
PY - 2021/8
Y1 - 2021/8
N2 - 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.
AB - 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.
KW - Correlation functions
KW - Networks
KW - Quantum phase transitions
KW - Random graphs
KW - Solvable lattice models
UR - http://www.scopus.com/inward/record.url?scp=85114396930&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85114396930&partnerID=8YFLogxK
U2 - 10.1088/1742-5468/ac150b
DO - 10.1088/1742-5468/ac150b
M3 - Article
AN - SCOPUS:85114396930
SN - 1742-5468
VL - 2021
JO - Journal of Statistical Mechanics: Theory and Experiment
JF - Journal of Statistical Mechanics: Theory and Experiment
IS - 8
M1 - 083103
ER -