2002/05/16 by V. Popkov, Vladislav Popkov, M. Ebrahim Fouladvand +3 · 26 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Ansatz #Bethe ansatz #Hamiltonian (control theory) #Integrable system #Mathematical physics #Mathematics #Physics #Pure mathematics #Quadratic equation #Quantum #Quantum many-body systems #Quantum mechanics #Random Matrices and Applications #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.1088/0305-4470/35/33/314
published in Journal of Physics A Mathematical and General 35(33), 7187-7204 (Institute of Physics) · 19 pages Latex
arxiv created 2002/05/16 · openalex publication_date 2002/08/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We propose a dynamical matrix product ansatz describing the stochastic dynamics of two species of particles with excluded-volume interaction and the quantum mechanics of the associated quantum spin chains, respectively. The time-dependent algebra which is obtained from the action of the Markov generator of the exclusion process (or quantum Hamiltonian of the spin chain, respectively) is given in terms of a set of quadratic relations. By analysing the permutation consistency of the induced cubic relations, we obtain sufficient conditions on the hopping rates (i.e. the quantum mechanical interaction constants) which allow us to identify integrable models. From the dynamical algebra we construct the quadratic algebra of Zamolodchikov type, the associativity of which is a Yang–Baxter equation. We also obtain directly from the dynamical matrix product ansatz the Bethe ansatz equations for the spectra of these models.