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Lattice Supersymmetry in the Open XXZ Model: An Algebraic Bethe Ansatz Analysis
We reconsider the open XXZ chain of Yang and Fendley. This model possesses a
lattice supersymmetry which changes the length of the chain by one site. We
perform an algebraic Bethe ansatz analysis of the model and derive the
commutation relations of the lattice SUSY operators with the four elements of
the open-chain monodromy matrix. Hence we give the action of the SUSY operator
on off-shell and on-shell Bethe states. We show that this action generally
takes one on-shell Bethe eigenstate to another. The exception is that a
zero-energy vacuum state will be a SUSY singlet. The SUSY pairings of Bethe
roots we obtain are analogous to those found previously for closed chains by
Fendley and Hagendorf by analysing the Bethe equations.Comment: 13 pages; dimension counting of SUSY operator image and kernel spaces
added; references update
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