Bethe ansatz solvability and supersymmetry of the $M_2$ model of single fermions and pairs

TL;DR

This paper explores a strongly-interacting fermion model with supersymmetry, identifying conditions for Bethe-ansatz solvability, analyzing ground states via cohomology, and connecting it to super-sine-Gordon models with exact gap scaling.

Contribution

It identifies a parameter submanifold where the model is Bethe-ansatz solvable and relates dynamic supersymmetries to this solvability, providing exact ground state and gap analysis.

Findings

Identified Bethe-ansatz solvable submanifold in parameter space.

Connected the lattice model to super-sine-Gordon at specific coupling.

Derived exact finite-size Bethe roots and gap scaling functions.

Abstract

A detailed study of a model for strongly-interacting fermions with exclusion rules and lattice $\mathcal N=2$ supersymmetry is presented. A submanifold in the space of parameters of the model where it is Bethe-ansatz solvable is identified. The relation between this manifold and the existence of additional, so-called dynamic, supersymmetries is discussed. The ground states are analysed with the help of cohomology techniques, and their exact finite-size Bethe roots are found. Moreover, through analytical and numerical studies it is argued that the model provides a lattice version of the $\mathcal N=1$ super-sine-Gordon model at a particular coupling where an additional $\mathcal N=(2,2)$ supersymmetry is present. The dynamic supersymmetry is shown to allow an exact determination of the gap scaling function of the model.