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

TL;DR

This paper develops an explicit matrix product ansatz for the steady state of a boundary driven XYZ spin-1/2 chain, valid in certain limits, extending the family of known separable eigenstates.

Contribution

It introduces a novel exact matrix product ansatz for the XYZ chain's steady state with arbitrary boundary conditions, using infinite-dimensional bidiagonal matrices.

Findings

Exact solution in the Zeno limit of infinite dissipation

Solution becomes exact in the thermodynamic limit of infinite chain length

Extends the family of separable eigenstates of the model

Abstract

We construct an explicit matrix product ansatz for the steady state of a boundary driven $XY\!Z$ spin-$\tfrac{1}{2}$ 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.