One‐Dimensional Quantum Markov Field With Commuting Hamiltonians

ABSTRACT This paper develops a comprehensive framework for one‐dimensional quantum Markov fields (QMFs) based on a family of commutative Hamiltonians. We present a detailed construction of a class of QMFs, initiated from a family of commuting Hamiltonians that perturb a product state on a quasi‐local algebra over a two‐sided one‐dimensional lattice. Furthermore, we establish an explicit expression for the mean entropy of translation‐invariant QMFs. This work contributes to advancing the theoretical understanding of exactly solvable quantum many‐body systems within the context of Markovian dynamics.