Supersymmetry Breaking in a Generalized Nicolai Model with Fermion Pairing

TL;DR

This paper introduces a supersymmetric lattice fermion model with a control parameter that breaks supersymmetry at finite and infinite scales, analyzes NG fermions, and clarifies ground-state properties.

Contribution

It presents a generalized Nicolai model with fermion pairing, demonstrating supersymmetry breaking and analyzing fermionic excitations and ground-state degeneracy.

Findings

Supersymmetry is broken for all finite g values.

NG fermions are gapless as shown by the single-mode approximation.

Ground-state degeneracy and flat bands are absent for generic g.

Abstract

We introduce a supersymmetric lattice fermion model that contains both fermion pairing and the interacting Nicolai model. This model possesses a single control parameter, $g$, introduced through the anticommutator of the supersymmetry generators (supercharge), and it is shown that supersymmetry is broken in both finite and infinite systems as long as $g$ is finite. Additionally, the single-mode approximation is employed to establish an upper bound on the dispersion relation of Nambu-Goldstone (NG) fermions, demonstrating their gaplessness. Finally, it is shown, through numerical and analytic calculations, that the anticipated extensive ground-state degeneracy and a zero-energy flat band does not occur for generic values of the parameter $g$.