Mott insulators and topological insulators are both important paradigms in the classification of quantum condensed matter systems. However, the insulating behaviour in each arises through very different mechanisms: a paramagnetic Mott insulator can be realized in the simplest one-band Hubbard model due to strong local interactions, while the bulk of a topological insulator derives its properties from the single-particle band structure. On the other hand, the boundary of a topological insulator hosts localized and protected metallic states.
In this seminar I will make a connection between these two seemingly different paradigms, showing that the Mott metal-insulator transition in the standard one-band Hubbard model can be understood as a topological phase transition. Our approach is inspired by the observation that the midgap pole in the self-energy of a Mott insulator resembles the spectral pole of the localized surface state in a topological insulator. We use NRG-DMFT to solve the infinite-dimensional Hubbard model, and represent the resulting local self-energy in terms of the boundary Green's function of an auxiliary tight-binding chain without interactions. The auxiliary system turns out to be of generalized SSH model type, with the Mott insulator being in the topological phase with a localized state living at the boundary between physical and auxiliary degrees of freedom. Within this picture, the Mott transition corresponds to a dissociation of domain walls.
[1] Phys. Rev. B 102, 081110(R) (2020)
