Spontaneous quantum Hall effect in quarter-doped Hubbard model on honeycomb lattice and its possible realization in quarter-doped graphene system

We show that as the result of the nesting property of the Fermi surface, the quarter-doped Hubbard model on honeycomb lattice is unstable with respect to the formation of a magnetic insulating state with nonzero spin chirality for infinitesimally small strength of electron correlation. The insulating state is found to be topological nontrivial and to have a quantized Hall conductance of $\sigma_{xy}=\frac{e^{2}}{h}$. We find the Fermi surface nesting is robust for arbitrary value of next-nearest-neighbor hopping integral. It is thus very possible that the quarter-doped graphene system will realize such an exotic ground state. We also show that the quarter-doped Hubbard model on honeycomb lattice is in exact equivalence in the weak coupling limit with the 3/4-filled Hubbard model on triangular lattice, in which similar effect is also observed.Comment: A proof of the exact equivalence between the quarter-doped Hubbard model on honeycomb lattice and the 3/4-filled Hubbard model on triangular lattice in the weak coupling limit is adde

A continuous family of fully-frustrated Heisenberg model on the Kagome lattice

We find that the antiferromagnetic Heisenberg model on the Kagome lattice with nearest neighboring exchange coupling(NN-KAFH) belongs to a continuous family of fully-frustrated Heisenberg model on the Kagome lattice, which has no preferred classical ordering pattern. The model within this family consists of the first, second and the third neighboring exchange coupling $J_{1}$, $J_{2}$, and $J_{3}$, with $J_{2}=J_{3}$. We find that when $-J_{1}\leq J_{2}=J_{3}\leq 0.2J_{1}$, the lowest band of $J(\mathbf{q})$, namely, the Fourier transform of the exchange coupling, is totally non-dispersive. Exact diagonalization calculation indicates that the ground state of the spin-$\frac{1}{2}$ NN-KAFH is locally stable under the perturbation of $J_{2}$ and $J_{3}$ when and only when $J_{2}=J_{3}$. Interestingly, we find that the same flat band physics is also playing an important role in the RVB description of the spin liquid state on the Kagome lattice. In particular, we show that the extensively studied $U(1)$ Dirac spin liquid state on the Kagome lattice can actually be generated from a continuous family of gauge inequivalent RVB mean field ansatz, which host very different mean field spinon dispersion.Comment: 5 pages, 7 figures. A correction made on the localized Wannier orbital of the flat band of the spinon mode