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In this article we study the relation between the eigenstates of openrational spin $\frac{1}{2}$ Heisenberg chains with different boundaryconditions. The focus lies on the relation between the spin chain with diagonalboundary conditions and the spin chain with triangular boundary conditions aswell as the class of spin chains that can be brought to such form by certainsimilarity transformations in the physical space. The boundary driven SymmetricSimple Exclusion Process (open SSEP) belongs to the latter. We derive atransformation that maps the eigenvectors of the diagonal spin chain to theeigenvectors of the triangular chain. This transformation yields an essentialsimplification for determining the states beyond half-filling. It allows tofirst determine the eigenstates of the diagonal chain through the Bethe ansatzon the fully excited reference state and subsequently map them to thetriangular chain for which only the vacuum serves as a reference state. Inparticular the transformed reference state, i.e. the fully excited eigenstateof the triangular chain, is presented at any length of the chain. It can bemapped to the steady state of the open SSEP. This results in a conciseclosed-form expression for the probabilities of particle distributions andcorrelation functions in the steady state. Further, the complete set ofeigenstates of the Markov generator is expressed in terms of the eigenstates ofthe diagonal open chain.

Eigenstates of triangularisable open XXX spin chains and closed-form solutions for the steady state of the open SSEP