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 field increases and, when the magnetic field is larger than a
Bc(U), the antiferromagnetic correlation shall be suppressed by the increased magnetic field. The impact of Zeeman field
B, Coulomb repulsion
U, and disorder $\mathrm{\ensuremath{\Delta}}$ 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
Uc=4.5, the increased interaction will suppress the intensity of this effect and here
Uc=4.5 coincides with the critical strength inducing the metal-Mott insulator transition in a clean system. Moreover, at a fixed magnetic field
B, strong interaction shall suppress the antiferromagnetic phase rather than promote it.
The dynamics of interacting particles in orbital magnetic fields are notoriously difficult to study, as this physics is inherently connected to electronic correlations in two-dimensional systems, for which no straightforward theoretical methods are available. Here, we report on the diffusive relaxation dynamics of two-dimensional interacting fermionic systems under a uniform magnetic field in the infinite temperature regime. We first show that the fermionic truncated Wigner approximation captures the equilibration dynamics unexpectedly well for intermediate interaction strengths when going beyond one dimension. This high accuracy holds at least for relatively small ladder systems, which are accessible to the Lanczos method that we use to benchmark the reliability of the Wigner approximation. We find that strong interactions, which exceed the hopping energy, suppress magnetic-field effects on diffusive transport. However, when the interactions are comparable to the kinetic energy, the diffusion is significantly reduced by the magnetic flux. This is observed for sufficiently large systems (above approximately 400 lattice sites), where finite-size effects weakly affect particle transport. We suggest that our results should be directly accessible on current optical lattice platforms.