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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi mathvariant="script">N</a:mi><a:mo>=</a:mo><a:mn>2</a:mn></a:mrow></a:math> supersymmetric <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:msub><c:mi>M</c:mi><c:mn>1</c:mn></c:msub></c:math> model, inheriting its integrability. The supersymmetric algebra additionally implies that the dynamics exhibit periodic revivals for specific initial states, including the <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:msub><d:mi mathvariant="double-struck">Z</d:mi><d:mn>2</d:mn></d:msub></d:math>-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 subthermal entanglement scaling at energies given by (plus or minus) square roots of integers and relate these to special eigenstates of the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:msub><f:mi>M</f:mi><f:mn>1</f:mn></f:msub></f:math> 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 nonergodic dynamics.