We elaborate the first theoretical realization of two dimensional itinerant topological magnons, based on the quarter filled Haldane-Hubbard model with a nearly-flat electron band. By using the exact diagonalization method with a projection onto this
band, we obtain the spin wave excitations over the itinerant ferromagnetic ground state. In the flatband limit, the excitation exhibits similar dispersion to the free electron band with Dirac magnons. The nonflatness of the electron band opens a topological gap at Dirac points and leads to an acoustic magnon band with a nonzero Chern number. We further show that tuning the sublattice Hubbard interactions or the next-nearest-neighbor hopping can induce a topological transition characterized by the gap closing and reopening, and the existence of the in-gap magnons on magnetic domain walls. We find an exact set of bases for magnons in the flatband limit constructed from sublattice particle-hole vectors and derive an effective model to explore the origin of the topological magnon which is attributed to the ``mass inversion mechanism.
Based on the mapping between $s=1/2$ spin operators and hard-core bosons, we extend the cluster perturbation theory to spin systems and study the whole excitation spectrum of the antiferromagnetic $J_{1}$-$J_{2}$ Heisenberg model on the square lattic
e. In the Neel phase for $J_{2}lesssim0.4J_{1}$, in addition to the dominant magnon excitation, there is an obvious continuum close to $(pi,0)$ in the Brillouin zone indicating the deconfined spin-1/2 spinon excitations. In the stripe phase for $J_{2}gtrsim0.6J_{1}$, we find similar high-energy two-spinon continuums at $(pi/2,pi/2)$ and $(pi/2,pi)$, respectively. The intermediate phase is characterized by a spectrum with completely deconfined broad continuum, which is attributed to a $Z_{2}$ quantum spin liquid with the aid of a variational-Monte-Carlo analysis.
We study the possible superconducting pairing symmetry mediated by spin and charge fluctuations on the honeycomb lattice using the extended Hubbard model and the random-phase-approximation method. From $2%$ to $20%$ doping levels, a spin-singlet $d_{
x^{2}-y^{2}}+id_{xy}$-wave is shown to be the leading superconducting pairing symmetry when only the on-site Coulomb interaction $U$ is considered, with the gap function being a mixture of the nearest-neighbor and next-nearest-neighbor pairings. When the offset of the energy level between the two sublattices exceeds a critical value, the most favorable pairing is a spin-triplet $f$-wave which is mainly composed of the next-nearest-neighbor pairing. We show that the next-nearest-neighbor Coulomb interaction $V$ is also in favor of the spin-triplet $f$-wave pairing.
We study the half-filled Hubbard model on the triangular lattice with spin-dependent Kitaev-like hopping. Using the variational cluster approach, we identify five phases: a metallic phase, a non-coplanar chiral magnetic order, a $120^circ$ magnetic o
rder, a nonmagnetic insulator (NMI), and an interacting Chern insulator (CI) with a nonzero Chern number. The transition from CI to NMI is characterized by the change of the charge gap from an indirect band gap to a direct Mott gap. Based on the slave-rotor mean-field theory, the NMI phase is further suggested to be a gapless Mott insulator with a spinon Fermi surface or a fractionalized CI with nontrivial spinon topology, depending on the strength of Kitaev-like hopping. Our work highlights the rising field that interesting phases emerge from the interplay of band topology and Mott physics.
We investigate the pairing symmetry in heavily overdoped Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$ based on the spin-fluctuation mechanism. The exotic octet nodes of the superconducting gap and the unusual evolution of the gap with doping observed by the rec
ent experiments are well explained in a unified manner. We demonstrate that the scatterings of electrons on the Fermi patches is mainly responsible for the incommensurate spin fluctuations and consequently the Fermi-surface-dependent multi-gap structure, since the Fermi level is close to the flat band. In addition, we find that a $d$-wave pairing state will prevail over the s-wave pairing state around the Lifshitz transition point.
