Magnetic phase transition in disordered interacting Dirac fermion systems via the Zeeman field

Abstract: Using the determinant quantum Monte Carlo method, we investigate the antiferromagnetic phase transition that is induced by the Zeeman field in a disordered interacting two-dimensional Dirac fermion system. At a fixed interaction strength $U$, the antiferromagnetic correlation is enhanced as the magnetic filed increases, and when the magnetic field is larger than a $B_{c}(U)$, the antiferromagnetic correlation shall be suppressed by the increased magnetic field. The impact of Zeeman field $B$, Coulomb repulsion $U$ and disorder $\Delta$ is not isolated. The intensity of magnetic field effect on the antiferromagnetic correlation shall be strongly suppressed by disorder. Differently, it will be promoted by weak interaction, but when $U$ becomes larger than $U_{c}=4.5$, the increased interaction will suppress the intensity of this effect, and here $U_{c}=4.5$ coincides with the critical strength inducing the metal-Mott insulator transition in clean system. Moreover, at a fixed magnetic field $B$, strong interaction shall suppress the antiferromagnetic phase rather than promote it.