In the first part of my talk, I will discuss the properties of fermionic microscopic models built from two coupled Su-Schrieffer-Heeger chains. We showed that such a system realizes all possible Altland-Zirnbauer symmetry classes. I will briefly discuss some general properties of these chain models that do not directly follow from the non-interacting classification table. In particular, we demonstrated that the non-interacting models that belong to Z classes can be adiabatically deformed into one another without changing the topological invariant as long as chiral symmetry is preserved. As a next step, I will discuss the effects of weak interactions on the topological properties of these chain models using bosonization and show that the chiral symmetry protects topology also in the interacting case.
In the second part of my talk, I will switch to a microscopic model of strongly interacting spinful fermions, where the gap is opened due to interactions. I will discuss the non-trivial topological properties of both insulating and metallic phases that emerge at the critical lines between gapped phases. I will discuss how these phases relate to and differ from single-particle topological phases.