Electronic instabilities of the extended Hubbard model on the honeycomb lattice from functional renormalization

TL;DR

This study uses the functional renormalization group to analyze the electronic instabilities in the extended Hubbard model on a honeycomb lattice, revealing dominant antiferromagnetic and charge-density wave phases, and challenging the stability of the topological Mott insulator.

Contribution

It provides a detailed momentum-resolved analysis of spin-1/2 fermions with extended interactions, highlighting the competition among various ordered phases.

Findings

Antiferromagnetic spin-density wave emerges with strong onsite repulsion.

Charge-density wave dominates with strong nearest-neighbor repulsion.

Charge-modulated ground state favored over topological Mott insulator with second-nearest neighbor interactions.

Abstract

Interacting fermions on the half-filled honeycomb lattice with short-range repulsions have been suggested to host a variety of interesting many-body ground states, e.g., a topological Mott insulator. A number of recent studies of the spinless case in terms of exact diagonalization, the infinite density matrix renormalization group and the functional renormalization group, however, indicate a suppression of the topological Mott insulating phase in the whole range of interaction parameters. Here, we complement the previous studies by investigating the quantum many-body instabilities of the physically relevant case of spin-1/2 fermions with onsite, nearest-neighbor and second-nearest-neighbor repulsion. To this end, we employ the multi-patch functional renormalization group for correlated fermions with refined momentum resolution observing the emergence of an antiferromagnetic spin-density wave and a charge-density wave for dominating onsite and nearest-neighbor repulsions, respectively. For dominating second-nearest neighbor interaction our results favor an ordering tendency towards a charge-modulated ground state over the topological Mott insulating state. The latter evades a stabilization as the leading instability by the additional onsite interaction.