Interplay of topology and interaction in an exactly solvable SSH-BCS-Hubbard chain

We propose an SSH-BCS-Hubbard chain model and theoretically study the interplay of topology and interaction therein. We obtain the exact solution of the model at the symmetric point. The exact solution reveals that the Hubbard interaction induces ${Z}₂$ symmetry breaking, which leads to the coexistence and competition of antiferromagnetic order and $\ensuremath{\eta}$-pairing order. The interaction splits the zero-energy states into in-gap states and destroys the symmetry-protected topological state of the SSH-BCS chain. However, the symmetry analysis reveals that the interacting topological state can exist for small Hubbard interaction and dimerization. The topological phase transition of the perturbed SSH-BCS-Hubbard is studied via the spectral ${Z}₂$ topological invariant. Our study uncovers a stable interacting topological state coexisting with symmetry-breaking induced intertwined orders.