  We investigate dynamics of the supersymmetric fermion lattice model defined
by Hermann Nicolai. We provide its local fermionic constants of motion that
exist infinitely many. These generate hidden local supersymmetries that the
Nicolai model possesses in addition to its defining dynamical supersymmetry.
The existence of such local constants directly implies the breaking ergodicity
of the model in the sense of Mazur. At zero temperature, there are infinitely
many degenerated classical ground states. We discuss these MBL-like properties.
First, we show the delocalization scenario proposed by De Roeck-Huveneers can
not naively apply to the Nicolai model at zero temperature despite its
disorder-free translation-invariant quantum interaction. Second, we discuss the
quantum integrability of the Nicolai model based on the proposal by
Caux-Mossel.
