Supersymmetry breakdown for an extended version of the Nicolai supersymmetric fermion lattice model

Sannomiya et al. have recently studied an extension of the Nicolai supersymmetric fermion lattice model, which is named “the extended Nicolai model.” The extended Nicolai model is parametrized by an adjustable constant $g\in \mathbb{R}$ in its defining supercharge and satisfies $\mathcal{N}=2$ supersymmetry. We show that for any nonzero $g$ the extended Nicolai model breaks supersymmetry dynamically, and the energy density of any homogeneous ground state for the model is strictly positive.