  The Su-Schrieffer-Heeger (SSH) model lays the foundation of many important
concepts in quantum topological matters. Since it tells one that topological
states may be distinguished by abelian geometric phases, a question naturally
arises as to what happens if one assembles two topologically distinct states.
Here, we show that a spin-dependent double-well optical lattice allows one to
couple two topologically distinct SSH chains in the bulk and realise a
glided-two-leg SSH model that respects the glide reflection symmetry. Such
model gives rise to intriguing quantum phenomena beyond the paradigm of a
traditional SSH model. It is characterised by Wilson line that requires
non-abelian Berry connections, and the interplay between the glide symmetry and
interaction automatically leads to charge fractionalisation without jointing
two lattice potentials at an interface. Our work demonstrates the power of
ultracold atoms to create new theoretical models for studying topological
matters.
