Lattice Supersymmetry in the Open XXZ Model: An Algebraic Bethe Ansatz Analysis

Abstract

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.

arXiv comment13 pages; dimension counting of SUSY operator image and kernel spaces added; references updated

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Cited by in corpus (5)

• Open XXZ chain and boundary modes at zero temperature
• On the transfer matrix of the supersymmetric eight-vertex model. II. Open boundary conditions
• On the transfer matrix of the supersymmetric eight-vertex model. I. Periodic boundary conditions
• The open XXZ chain at $\Delta =-1/2$ and the boundary quantum Knizhnik-Zamolodchikov equations
• Lattice SUSY for the DiSSEP at ${\lambda }^2=1$ (and ${\lambda }^2=-3$)