Exact steady state manifold of a boundary driven spin-1 Lai–Sutherland chain

We present an explicit construction of a family of steady state density matrices for an open integrable spin-1 chain with bilinear and biquadratic interactions, also known as the Lai–Sutherland model, driven far from equilibrium by means of two oppositely polarizing Markovian dissipation channels localized at the boundary. The steady state solution exhibits n+1n+1 fold degeneracy, for a chain of length n  , due to existence of (strong) Liouvillian U(1)U(1) symmetry. The latter can be exploited to introduce a chemical potential and define a grand canonical nonequilibrium steady state ensemble. The matrix product form of the solution entails an infinitely-dimensional representation of a non-trivial Lie algebra (semidirect product of sl2sl2 and a non-nilpotent radical) and hints to a novel Yang–Baxter integrability structure.