Solitary waves of attracting SU(N) fermions

We study the formation, dynamics, and disorder robustness of bound states in attractively interacting SU(N) fermions on a one-dimensional ring lattice. Using exact diagonalization in fixed-momentum sectors and Bethe ansatz exact results as a guide, we resolve the many-body spectrum into bands related to the possible partitions of the particles into bound composites, and characterize their internal structure also through density-density and N-body correlations. A pinning quench protocol reveals a transition from dispersive spreading to dynamical localization as the attractive interaction increases relative to the single-particle hopping. We find that the bound state dynamics for one-particle per component occurs as a many-body quantum walk similar to that of a single particle with a re-normalized effective mass. Such a property, that is the quantum version of the shape-preserving motion of classical solitons, can provide the dynamical signature of the fermionic solitary waves. We probe the robustness of the fermionic bound-state dynamics under on-site disorder.