Dynamic Lattice Supersymmetry in gl(n|m) Spin Chains

Abstract

Supersymmetry operators that change a spin chain's length have appeared in numerous contexts, ranging from the AdS/CFT correspondence to statistical mechanics models. In this article, we present, via an analysis of the Bethe equations, all homogeneous, rational and trigonometric, integrable gl(n|m) spin chains for which length-changing supersymmetry can be present. Furthermore, we write down the supercharges explicitly for the simplest new models, namely the sl(n|1) spin chains with the (n-1)-fold antisymmetric tensor product of the fundamental representation at each site and check their compatibility with integrability.

25 pages. v2: minor changes, typos corrected, to appear in J.Stat.Phys

References in corpus (2)

• On the Hopf algebra structure of the AdS/CFT S-matrix
• Singular solutions, repeated roots and completeness for higher-spin chains

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• Lattice SUSY for the DiSSEP at ${\lambda }^2=1$ (and ${\lambda }^2=-3$)