EXACT SPECTRAL PROBLEM SOLUTION FOR A LATTICE MANY-BODY SYSTEM WITH A FLOW

The matrix product state approach to interacting many-body systems was inspired by the quantum inverse scattering method and developed to describe the stationary behaviour. Driven diffusive systems have the intriguing feature that the properties of the steady state strongly depend on the boundary rates. We have shown that the boundary conditions of the asymmetric simple exclusion process on a lattice define the boundary symmetry as a generalized Onsager algebra, a coideal subalgebra of the bulk quantum affine U-q((s (u) over cap (2)). We implement algebraic Bethe Ansatz based on the zeros of the Askey-Wilson polynomials to diagonalize the transition rate matrix of the process and find the complete spectrum. The condition for the constructed irreducible finite-dimensional representation of the boundary algebra can be related to the Gallavotti-Cohen symmetry.