SU(N) fractional quantum Hall effects in topological flat bands

We study $N$-component interacting particles (hardcore bosons and fermions) loaded in topological lattice models with SU$(N)$-invariant interactions based on density matrix renormalization group method. By tuning the interplay of interspecies and intraspecies interactions, we demonstrate that a class of SU$(N)$ fractional quantum Hall states can emerge at fractional filling factors $\nu=N/(N+1)$ for bosons ($\nu=N/(2N+1)$ for fermions) in the lowest Chern band, characterized by the nontrivial fractional Hall responses and the fractional charge pumping. Moreover, we establish a topological characterization based on the $\mathbf{K}$ matrix, and discuss the close relationship to the fractional quantum Hall physics in topological flat bands with Chern number $N$.Comment: 9 pages, 12 figure

Orbital Magnetism Induced by Heat Currents in Mott insulators

We derive the effective heat current density operator for the strong-coupling regime of Mott insulators. Similarly to the case of the electric current density, the leading contribution to this effective operator is proportional to the local scalar spin chirality $\hat{\chi}_{jkl}= \mathbf{S}_l\cdot\left(\mathbf{S}_j\times \mathbf{S}_k\right)$. This common form of the effective heat and electric current density operators leads to a novel cross response in Mott insulators. A heat current induces a distribution of orbital magnetic moments in systems containing loops of an odd number of hopping terms. The relative orientation of the orbital moments depends on the particular lattice of magnetic ions. This subtle effect arises from the symmetries that the heat and electric currents have in common.Comment: 4.3 pages and 3 figure

Bubble and Skyrmion Crystals in Frustrated Magnets with Easy-Axis Anisotropy

We clarify the conditions for the emergence of multiple-${\bf Q}$ structures out of lattice and easy-axis spin anisotropy in frustrated magnets. By considering magnets whose exchange interaction has multiple global minima in momentum space, we find that both types of anisotropy stabilize triple-${\bf Q}$ orderings. Moderate anisotropy leads to a magnetic field-induced skyrmion crystal, which evolves into a bubble crystal for increasing spatial or spin anisotropy. The bubble crystal exhibits a quasi-continuous (devil's staircase) temperature dependent ordering wave-vector, characteristic of the competition between frustrated exchange and strong easy-axis anisotropy.Comment: 9 pages, 10 figure

Ab Initio Simulation of the Nodal Surfaces of Heisenberg Antiferromagnets

The spin-half Heisenberg antiferromagnet (HAF) on the square and triangular lattices is studied using the coupled cluster method (CCM) technique of quantum many-body theory. The phase relations between different expansion coefficients of the ground-state wave function in an Ising basis for the square lattice HAF is exactly known via the Marshall-Peierls sign rule, although no equivalent sign rule has yet been obtained for the triangular lattice HAF. Here the CCM is used to give accurate estimates for the Ising-expansion coefficients for these systems, and CCM results are noted to be fully consistent with the Marshall-Peierls sign rule for the square lattice case. For the triangular lattice HAF, a heuristic rule is presented which fits our CCM results for the Ising-expansion coefficients of states which correspond to two-body excitations with respect to the reference state. It is also seen that Ising-expansion coefficients which describe localised, $m$-body excitations with respect to the reference state are found to be highly converged, and from this result we infer that the nodal surface of the triangular lattice HAF is being accurately modeled. Using these results, we are able to make suggestions regarding possible extensions of existing quantum Monte Carlo simulations for the triangular lattice HAF.Comment: 24 pages, Latex, 3 postscript figure