Local basis for interacting topological bands

The discovery of correlated states in moire materials has challenged the established methods of projecting interactions into a local Wannier basis due to topological obstructions that manifest in extended interactions. This difficulty can sometimes be evaded by decomposing the band into a basis of extended itinerant states and a lattice of local states, using the heavy fermion prescription. We revisit this framework by systematically identifying the dominant interaction channels guided by the eigenvalues of the projected density operator. This approach can be applied both to tight-binding and continuum models, allowing us to identify a hierarchy in interaction scales that can be universally used to reduce the Hilbert space dimension and determine an appropriate local basis for modeling electronic correlations in interacting topological materials.