Topological Phases of the Interacting SSH and Kitaev Models on the Bethe Lattice

Topological phases of matter have been intensely studied in recent years, but there still remain a number of open questions regarding the interplay of topology and strong interactions in condensed matter systems, including the role of topological invariants. Two prototypical models in one dimension exhibiting non-trivial topological phases are the SSH model and the Kitaev chain. Here we study generalizations of these models on the Bethe lattice, showing that topological phases with bulk zero-modes can be realized in higher dimensions. We then consider interacting versions of these Bethe SSH and Kitaev models with local Hubbard interactions, U. These topological Hubbard models are solved exactly in infinite dimensions at T=0 using dynamical mean field theory with the numerical renormalization group as an impurity solver.

For the Bethe SSH Hubbard model with interactions U<U_c below a critical strength, bulk gapped sites at U=0 develop a power-law pseudogap density of states, while sites with topological zero-mode poles at U=0 are augmented by power-law diverging quasiparticle Kondo peaks. A bulk Mott insulating phase is realized for U>U_c. A method of characterizing the topological phases of the systems in the presence of interactions based on their Green's functions is discussed.