Influence of Landau-Level Mixing on the Quantum Hall Phase Diagram in Neutral Graphene

In the presence of a strong magnetic field, the ground state of neutral graphene was identified as the canted antiferromagnet through non-local charge and magnon transport experiments. This understanding has been recently challenged by STM experiments. We note that the difference in the dielectric screening environments between these experiments could affect the phase diagram, particularly through Landau-level mixing. In this study, we explore the self-consisntent mean-field phase diagram of neutral graphene in a 5-dimensional parameter space without evoking the zeroth-Landau level projection. This permits a non-perturbative treatment of the Landau level mixing effect and accounts for the previously overlooked Dirac sea's contribution to the total energy. Our parameter space encompasses the dielectric screening constant, two intra-sublattice short-range interactions due to electron-electron interaction, and two inter-sublattice short-range interactions originating from electron-phonon interactions. Our results indicate that the spin-valley order of the zeroth Landau level can induce secondary ordering within the Hilbert space spanned by electron-like Landau level |+N> and hole-like Landau level |-N>. These theoretical findings provide valuable context and clarity to the experimental findings