  We analyze the static and dynamical properties of a one-dimensional
topological lattice, the fermionic Su-Schrieffer-Heeger model, in the presence
of on-site interactions. Based on a study of charge and spin correlation
functions, we elucidate the nature of the topological edge modes, which
depending on the sign of the interactions, either display particles of opposite
spin on opposite edges, or a pair and a holon. This study of correlation
functions also highlights the strong entanglement that exists between the
opposite edges of the system. This last feature has remarkable consequences
upon subjecting the system to a quench, where an instantaneous edge-to-edge
signal appears in the correlation functions characterizing the edge modes.
Besides, other correlation functions are shown to propagate in the bulk
according to the light-cone imposed by the Lieb-Robinson bound. Our study
reveals how one-dimensional lattices exhibiting entangled topological edge
modes allow for a non-trivial correlation spreading, while providing an
accessible platform to detect spin-charge separation using state-of-the-art
experimental techniques.
