Decomposing interaction length scales in the Aubry-Andre-Hubbard model

The Aubry-Andre model is one of the few exactly solvable models that exhibit localization of many-body states. This solvability is underwritten by the self-duality of the model. Adding Hubbard interactions breaks this self-duality and makes it difficult to study the interacting model outside of a perturbative regime. Instead, we show that the Aubry-Andre-Hubbard (AAH) model is dual to a model with local-in-momentum space interactions - the Aubry-Andre-Hatsugai-Kohmoto (AAHK) model. We show how, by systematically decomposing the Hubbard interaction into clusters at a given length scale, it is possible to interpolate between the AAH and AAHK models. By benchmarking the ground state properties of this scheme to DMRG calculations, we show that the optimal length scale is controlled by the Aubry-Andre potential strength.