The Mott transition as a topological phase transition

We show that the Mott metal-insulator transition in the standard one-band Hubbard model can be understood as a topological phase transition. The approach is inspired by the observation that the Mott pole in the self-energy is pinned throughout the insulating phase, similar to the zero-energy spectral pole corresponding to a localized surface state in topological systems. 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. We find a rich structure in the parameters of the auxiliary chain, which we show are of generalized SSH model type. The Mott transition corresponds to a topological phase transition in this auxiliary system, characterized by its analytic properties. We devise simple toy models for the auxiliary chains that capture the basic physics of the metallic and insulating Hubbard model phases, as well as in the scaling limit near the transition.