A staggered fermion chain with supersymmetry on open intervals

A strongly-interacting fermion chain with supersymmetry on the lattice and open boundary conditions is analysed. The local coupling constants of the model are staggered, and the properties of the ground states as a function of the staggering parameter are examined. In particular, a connection between certain ground-state components and solutions of non-linear recursion relations associated with the Painlev\'e VI equation is conjectured. Moreover, various local occupation probabilities in the ground state have the so-called scale-free property, and allow for an exact resummation in the limit of infinite system size.