Periodic revivals from supersymmetry in a fermionic kinetically constrained model

Supersymmetry provides a natural playground for the construction of dynamically constrained lattice fermion models. We here illustrate how supersymmetry can be used to construct a fermionic equivalent of the PXP model with an adjustable chemical potential. This model is closely related to the $\mathcal{N} = 2$ supersymmetric $M_1$ model, inheriting its integrability. The supersymmetric algebra additionally implies that the dynamics exhibit periodic revivals for specific initial states, including the $\mathbb{Z}_2$-ordered (every second site occupied) product state. These dynamics are reminiscent to those of the PXP model, a paradigmatic effective model in the field of quantum many-body scars. We draw a further parallel by uncovering eigenstates obeying sub-thermal entanglement scaling at energies given by (plus or minus) square roots of integers and relate these to special eigenstates of the $M_1$ model. While we focus on a concrete model, our proposed approach is applicable to more general supersymmetric algebras, where it is expected to lead to non-ergodic dynamics.