Phase Diagram of the half-filled extended Hubbard model on a honeycomb lattice

The competition between interactions in fermionic systems usually gives rise to a multitude of interesting phases, which are often sensitive to the underlying lattice geometry.

The recent discovery of correlated insulating phases and superconductivity in magic-angle twisted bilayer graphene (TBG) has spawned renewed interest in the study of strongly correlated phenomena on a honeycomb lattice (HC). From a theoretical perspective, the Extended Hubbard Model (EHM) is one of the simplest models describing emergent magnetic, charge, and superconducting orders in electronic systems. Indeed, while a repulsive on-site interaction, U > 0, favors the formation of magnetic moments and their effective coupling, the presence of a repulsive nearest-neighbor interaction, V > 0, enhances charge correlations, thus favoring arrangements of doubly occupied sites. If one allows for attractive interactions in either the on-site or the nearest-neighbor channels, or both, one may wonder which pairing states may be stabilized in the ground state. With this in mind, here we use determinant quantum Monte Carlo simulations to probe the whole (i.e., the four possible combinations of U and V being positive or negative) phase diagram of the half-filled EHM on a HC lattice. The calculations have been carried out with complex Hubbard-Stratonovich (HS) auxiliary fields to yield sign-free simulations in the range |V| ≤ |U|/3, in which case structure factors probing the ordered phases have been fed into correlation ratios; this allows for precise determination of critical boundaries through finite-size scaling analyses. Outside this region we use real HS fields and resort to additional local quantities, such as double occupancy and the average sign of the product of fermionic determinants, to determine the boundary of the CDW phase with a high degree of confidence. We have also established that only s-wave superconductivity is present, in marked contrast with the square lattice where d-wave pairs can be preferably stabilized. Further, as |V| increases, the AFM phase demands larger values of U to stabilize. As expected, for sufficiently small V < 0 a phase separated region dominates the whole diagram for all U.