Condensate and Soliton stability in a 1D lattice with density-dependent hopping

The nonlinear Schrodinger equation is a ubiquitous model, providing insight into a variety of systems, ranging from nonlinear optics to Bose-Einstein condensates. Motivated by a previously proposed Floquet protocol, we have investigated a discrete nonlinear Schrodinger equation where the role of the interaction is played by a density-dependent hopping, equivalent to a dynamical gauge field. The few particle physics of this system have been previously studied and found to exhibit topology induced by the interaction. Here we explore the many-body physics. We find that in the limit of the low gauge coupling, the ground state is described by a plane wave while for large gauge couplings, the ground state corresponds to a soliton. Uniquely this system has soliton solutions while the plane wave spectrum is completely non-interacting. We explore the stability of the condensate plane waves to linear perturbations from both the classical linearization and the quantum Bogoliubov transformation. Finally, we elucidate unique nonreciprocal physics brought by non-Hermiticity in the gauge coupling.