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

TL;DR

This paper analyzes the lattice supersymmetry of the open XXZ chain using algebraic Bethe ansatz, revealing how SUSY operators act on Bethe states and identifying SUSY singlet states.

Contribution

It provides a detailed algebraic Bethe ansatz analysis of the lattice supersymmetry in the open XXZ model, including operator actions and SUSY pairings of Bethe roots.

Findings

SUSY operators change the chain length by one site.

SUSY generally maps Bethe states to other eigenstates.

Zero-energy vacuum states are SUSY singlets.

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.