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Journal of Physics A Mathematical and General

Integrable Zn*ZnBelavin model with non-trivial boundary terms

Rui‐Hong Yue, Yi-Xin Chen

Published Jun 21, 1993• 8 citations
Publisher

Abstract

The open chain corresponding to the Belavin model (1982) is constructed by generalizing Skylanin's formalism (1988) to the case of the R-matrix with Z n symmetry.
DOI
10.1088/0305-4470/26/12/033

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In this paper, we address the problem of Yang-Baxter integrability of doubled quantum circuit of qubits (spins 1/2) with open boundary conditions where the two circuit replicas are only coupled at the left or right boundary. We investigate the cases where the bulk is given by elementary six vertex unitary gates of either the free fermionic XX type or interacting XXZ type. By using the Sklyanin’s construction of reflection algebra, we obtain the most general solutions of the boundary Yang-Baxter equation for such a setup. We use this solution to build, from the transfer matrix formalism, integrable circuits with two step discrete time Floquet (aka brickwork) dynamics. We prove that, only if the bulk is a free-model, the boundary matrices are in general non-factorizable, and for particular choice of free parameters yield non-trivial unitary dynamics with boundary interaction between the two chains. Then, we consider the limit of continuous time evolution and we give the interpretation of a restricted set of the boundary terms in the Lindbladian setting. Specifically, for a particular choice of free parameters, the solutions correspond to an open quantum system dynamics with the source terms representing injecting or removing particles from the boundary of the spin chain.