Super Lax pairs and infinite symmetries in the 1/r² system

Abstract

We present an algebraic structure that provides an interesting and novel link between supersymmetry and quantum integrability. This structure underlies two classes of models that are exactly solvable in one dimension and belong to the 1/r² family of interactions. The algebra consists of the commutation between a "super-Hamiltonian" and two other operators, in an enlarged Hilbert space. These reduce to quantal Ordered Lax equations when projected onto the original subspace, and to a statement about the "Harmonic Lattice Potential" structure of the Lax operator, leading to a highly automatic proof of the integrability of these models and to an interesting hierarchy of new models.