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Using finite-temperature determinantal quantum Monte Carlo calculations, were-examine the pairing susceptibilities in the Hubbard model on the honeycomblattice, focusing on doping levels onto and away from the van Hove singularity(VHS) filling. For this purpose, electronic densities of $0.75$ (at thehole-doping VHS) and $0.4$ (well below the VHS) are considered in detail, wheredue to a severe sign problem at strong coupling strengths, we focus on the weakinteraction region of the Hubbard model Hamiltonian. From analyzing thetemperature dependence of pairing susceptibilities in various symmetrychannels, we find the singlet $d$+$id$-wave to be the dominant pairing channelboth at and away from the VHS filling. We furthermore investigate theelectronic susceptibility to a specific chiral spin density wave (SDW) order,which we find to be similarly relevant at the VHS, while it extenuates upondoping away from the VHS filling.

Pairing and chiral spin density wave instabilities on the honeycomb lattice: a comparative quantum Monte Carlo study