简介: |
How interactions turn a partially filled electron band into an insulating state is an important question of strong correlation physics. We perform extensive projector determinant quantum Monte-Carlo simulations on the SU(N) Hubbard models to address this problem.
At half-filling, i.e., the average fermion number N/2 per site, the antiferromagnetic (AF) orders in the square lattice start from the weak U regime for both SU(4) and SU(6) cases. They exhibit non-monotonic dependence on U: After reaching maxima at intermediate interaction strengths, they decrease as U further increases. Roughly at the same interaction strengths, the single-particle gap evolves from very small values to linearly increase with U, marking the onset of Mott physics. For the SU(6) case, the AF order vanishes at the critical value of U=13.3 exhibiting the critical exponents of ν=0.60 and η=0.44. As U further increases, the valence bond solid (VBS) ordering appears. In contrast, the SU(4) and SU(6) Hubbard models of Dirac fermions in the honeycomb lattice andπ-flux square lattice exhibit the transition from the Dirac semi-metal phase to the VBS state. We also investigated how interaction effects scale with N in the 1D SU(N) Hubbard models at half-filling. As N increases, weak and strong interacting systems are driven to a crossover region, but from opposite directions as a convergence of itinerancy and Mottness. The crossover region exhibits nearly N-independent physical quantities, including the relative bandwidth, Fermi distribution, and the spin structure factor.
Ref.
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