Solitons in lattice field theories via tight-binding supersymmetry

Reflectionless potentials play an important role in constructing exact solutions to classical dynamical systems, non-perturbative of various large-N field theories, and closely related solitonic the Bogoliubov-de Gennes equations theory superconductivity. These rely on inverse scattering method, which reduces these seemingly unrelated problems identifying reflectionless auxiliary one-dimensional quantum problem. There are several ways potentials, one is mechanical supersymmetry (SUSY). In this paper, motivated by recent experimental platforms, we generalize framework develop a solitons lattice versions interacting theories. Our analysis hinges use trace identities, relations connecting potential equation motion data. For discrete Schr\"odinger operator, such identities well known, derive new set for Dirac operator. We then Gross-Neveu chiral (Nambu-Jona-Lasinio) model show that correspond associated with models significance as they equivalent mean-field superconductor. To explicitly construct solitons, supersymmetric mechanics tight-binding models. matrix transformation exists maps isospectral shares same structure properties. The corresponding soliton have both modulated hopping onsite potential; compute topological non-topological bound state spectra aforementioned