Magnetism of finite graphene samples: Mean-field theory compared with exact diagonalization and quantum Monte Carlo simulations

The magnetic properties of graphene on finite geometries are studied using a self-consistent mean-field theory of the Hubbard model. This approach is known to predict ferromagnetic edge states close to the zigzag edges in single-layer graphene quantum dots and nanoribbons. In order to assess the accuracy of this method, we perform complementary exact diagonalization and quantum Monte Carlo simulations. We observe good quantitative agreement for all quantities investigated provided that the Coulomb interaction is not too strong.

Figure 1

(Color online) Mean-field result for the edge magnetization of a hexagonal graphene quantum dot with $N=96$ sites and zigzag edges (at half-filling and with $U=2t$).

Figure 2

(Color online) Comparison MFT-ED for the finite-size system of 16 sites sketched in the inset of the top panel at half-filling. The bottom panel shows the total staggered magnetization $M_{\text{s}}$ in the main panel and the $z$-component $M_{\text{s}}^z$ in the inset.

Figure 3

(Color online) Comparison MFT-QMC for a system with periodic boundary conditions and $N=162$ sites at half-filling. QMC error bars are smaller than the size of the symbols.