Time-dependent matrix product ansatz for interacting reversible dynamics

Katja Klobas, Marko Medenjak, Tomaž Prosen +1 more

Sangwoo S. Chung, Kuei Sun, C. J. Bolech

Anderson Almeida Ferreira, Francisco Castilho Alcaraz

Belal Abouraya, Jirawat Saiphet, Fedor Jelezko +1 more

Tomohiro Sasamoto, Miki Wadati

A new type of dynamic matrix product ansatz is proposed. The states which satisfy the "imaginary time" Schrödinger equation are represented in the form of products of time-dependent and time-independent matrices. From the algebra among the matrices, the Bethe ansatz equation is derived for the asymmetric exclusion process and the XXZ spin chain under the periodic boundary condition.

Vladislav Popkov, M. Ebrahim Fouladvand, Gunter Markus Schutz

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.