In view of the recent experimental facts in the iron-pnictides, we make a proposal that the itinerant electrons and local moments are simultaneously present in such multiband materials. We study a minimal model composed of coupled itinerant electrons and local moments to illustrate how a consistent explanation of the experimental measurements can be obtained in the leading order approximation. In this mean-field approach, the spin-density-wave (SDW) order and superconducting pairing of the itinerant electrons are not directly driven by the Fermi surface nesting, but are mainly induced by their coupling to the local moments. The presence of the local moments as independent degrees of freedom naturally provides strong pairing strength for superconductivity and also explains the normal-state linear-temperature magnetic susceptibility above the SDW transition temperature. We show that this simple model is supported by various anomalous magnetic properties and isotope effect which are in quantitative agreement with experiments.

We study several different Z2 topological ordered states in frustrated spin systems. The effective theories for those different Z2 topological orders all have the same form -a Z2 gauge theory which can also be written as a mutual U (1) × U (1) Chern-Simons theory. However, we find that the different Z2 topological orders are reflected in different projective realizations of lattice symmetry in the same effective mutual Chern-Simons theory. This result is obtained by comparing the groundstate degeneracy, the ground-state quantum numbers, the gapless edge state, and the projective symmetry group of quasi-particles calculated from the slave-particle theory and from the effective mutual Chern-Simons theories. Our study reveals intricate relations between topological order and symmetry.

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In this paper, we investigate the topological Hubbard model -the spinful Haldane model with onsite interaction on honeycomb lattice with spin rotation symmetry by using slave-rotor approach and find that chiral spin liquid exists in such a correlated electron system of the intermediate coupling region. By considering the anyon nature of excitations, chiral spin liquid may be the ground state of the topological Hubbard model. The low energy physics is basically determined by its Chern-Simons gauge theory.

A mutual-Chern-Simons Lagrangian is derived as a minimal field theory description of the phasestring model for doped antiferromagnets. Such an effective Lagrangian is shown to retain the full symmetries of parity, time-reversal, and global SU(2) spin rotation, in contrast to conventional Chern-Simons theories where first two symmetries are usually broken. Two ordered phases, i.e., antiferromagnetic and superconducting states, are found at low temperatures as characterized by "dual" Meissner effects and dual flux quantization conditions due to the mutual-Chern-Simons gauge structure. A "dual" confinement in charge/spin degrees of freedom occurs such that no true spincharge separation is present in these ordered phases, but the spin-charge separation/deconfinement serves as a driving force in the unconventional phase transitions of these ordered states to disordered states.