The eight-vertex model and lattice supersymmetry

Abstract

We show that the XYZ spin chain along the special line of couplings J_xJ_y+J_xJ_z+J_yJ_z=0 possesses a hidden N=(2,2) supersymmetry. This lattice supersymmetry is non-local and changes the number of sites. It extends to the full transfer matrix of the corresponding eight-vertex model. In particular, it is shown how to derive the supercharges from Baxter's Bethe ansatz. This analysis leads to new conjectures concerning the ground state for chains of odd length. We also discuss a correspondence between the spectrum of this XYZ chain and that of a manifestly supersymmetric staggered fermion chain.

40 pages, 6 figures, TikZ

References in corpus (7)

• The eight-vertex model and Painleve VI
• Exact ground states of a staggered supersymmetric model for lattice fermions
• Exact and simple results for the XYZ and strongly interacting fermion chains
• Combinatorial point for higher spin loop models
• The su(2|3) Undynamic Spin Chain
• Detailed analysis of the continuum limit of a supersymmetric lattice model in 1D
• An elliptic current operator for the 8 vertex model

Cited by in corpus (22)

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• Supersymmetric lattice fermions on the triangular lattice: superfrustration and criticality
• Special polynomials related to the supersymmetric eight-vertex model: A summary
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• Lattice Supersymmetry in the Open XXZ Model: An Algebraic Bethe Ansatz Analysis
• Order and supersymmetry at high filling zero energy states on the triangular lattice
• 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
• A staggered fermion chain with supersymmetry on open intervals
• Eigenstate entanglement entropy in the integrable spin-$\frac{1}{2}$ XYZ model
• Spinon excitations in the spin-1 XXZ chain and hidden supersymmetry
• Elliptic pfaffians and solvable lattice models
• A Pedestrian's Way to Baxter's Bethe Ansatz for the Periodic XYZ Chain
• Original electric-vertex formulation of the symmetric eight-vertex model on the square lattice is fully non-universal
• Fusion rule in conformal field theories and topological orders: A unified view of correspondence and (fractional) supersymmetry and their relation to topological holography
• Sum rules for the supersymmetric eight-vertex model
• Topological Quantum Computation on Supersymmetric Spin Chains
• Boundary effects on the supersymmetric sine-Gordon model through light-cone lattice approach
• A Combinatorial Description of Certain Polynomials Related to the XYZ Spin Chain. II. The Polynomials $p_n$
• Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
• Lattice SUSY for the DiSSEP at ${\lambda }^2=1$ (and ${\lambda }^2=-3$)