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Integrable Markov processes and quantum spin chains. (English) Zbl 1140.82319

Summary: A set of Markov processes corresponding to systems of hard-core particles interacting along the line are shown to be solvable via a dynamic matrix product ansatz (DMPA). We show that quantum spin Hamiltonians can be treated by the DMPA as well, and demonstrate how the DMPA, originally formulated for systems with open ends, works for periodic systems.

MSC:

82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics
82C23 Exactly solvable dynamic models in time-dependent statistical mechanics