Boundary driven $XYZ$ chain: Exact inhomogeneous triangular matrix product ansatz

Abstract

We construct an explicit matrix product ansatz for the steady state of a boundary driven $XYZ$ spin-$\frac{1}{2}$ chain for arbitrary local polarizing channels at the chain's ends. The ansatz, where the Lax operators are written explicitly in terms of infinite-dimensional bidiagonal (triangular) site-dependent matrices, becomes exact either in the (Zeno) limit of infinite dissipation strength, or thermodynamic limit of infinite chain length. The solution is based on an extension of the newly discovered family of separable eigenstates of the model.

5 pages, 2 Figures

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• Bethe-ansatz diagonalization of steady state of boundary driven integrable spin chains
• Dissipative cooling towards phantom Bethe states in boundary driven XXZ spin chain