Interplay between interaction and topology in Hubbard-Haldane model

The interplay between topology and interaction has been brought to foreground by the experiments on twisted bilayer Graphene and twisted metal dichalcogenides over the last few years. At the heart of the issue is the conflict between the Mott physics (limit of strong on-site Coulomb repulsion) and the topology. This leads to a correlated insulator or a bad metal rather than a Mott insulator, a regime that is also called Mott metallicity. Doping such a correlated insulator is of interest for the observation of superconductivity in such systems.

We use a novel representation of correlated electrons in terms of fermionic spinons and slave bosons which enable us to study problems with weak to strong Coulomb interaction. After a comparison to existing dynamical mean-field theory and slave spins on square lattice, we apply this method to study the interplay between topology and interaction in the Hubbard-Haldane model. In this system, the effect of interaction on the electronic density of states is beyond a simple renormalization of the wavefunction and the spinon bandwidth. We probe this physics by presenting both magnetic and pair susceptibility at and away from charge neutrality.