In this paper, we develop an effective mutual Chern-Simons Landau-Ginzburg MCSLG theory to describe the continuous topological quantum phase transition TQPT. In particular, we consider the TQPT etween a spin-polarized phase a state without topological order and a Z2 topologically ordered state. The TQPT is not induced by spontaneous symmetry breaking. Instead the Z2 topological order is broken down by the condensation of Z2 charged quasiparticles. By generalizing the hierarchy theory of fractional quantum Hall effect to Z2 topological order, we show that the TQPT belongs to the universal class of three-dimensional Ising phase transition. In the end, we applied the MCSLG theory to the toric code model.

In this paper, based on the formulation of O (3) non-linear model, we study two dimensional−flux Hubbard model at half-filling. A quantum non-magnetic insulator is explored near metalinsulator transition that may be a possible candidate of spin liquid state. Such quantum nonmagnetic insulator on square lattice is not induced by frustrations. Instead, it originates from quantum spin fluctuations with relatively small e ective spin-moments. In the strong coupling limit, our results of spin velocity and spin order parameter agree with results obtained from earlier calculations.

In this paper a duality between the d=2 Wen-plaquette model in a transverse field and the d=1 Ising model in a transverse field is used to learn the nature of the quantum phase transition (QPT) between a spin-polarized phase and a topological ordered state with the string-net condensation. The QPT is not induced by spontaneous symmetry breaking and there are no conventional Landautype local order parameters. Instead the string-like non-local order parameters are introduced to describe the QPT. In particular, the duality character between the open-string and closed string for the QPT are explored.

We propose a model of coupled local moments and itinerant electrons to describe the iron-based superconductors. Here the spin-density-wave (SDW) order of the itinerant electrons is not driven by Fermi surface nesting but is induced by the Hund's rule coupling with the local moments. The superconducting pairing is of the same origin whose strength can reach strong coupling. The existence of the local moments is supported by various anomalous magnetic properties which are in quantitative agreement with experiments.

In this paper, by using two dimensional (2D) Hubbard models with-flux phase and that on a hexagonal lattice as examples, we explore spin-charge-separated solitons in nodal antiferromagnetic (AF) insulator-an AF order with massive Dirac fermionic excitations (see detail in the paper). We calculate fermion zero modes and induced quantum numbers on solitons (half skyrmions) in the continuum limit, which are similar to that in the quasi one-dimensional conductor polyacetylene (CH)x and that in topological band insulator. In particular, we find some novel phenomena: thanks to an induced staggered spin moment, a mobile half skyrmion becomes a fermionic particle; when a hole or an electron is added, the half skyrmion turns into a bosonic particle with charge degree of freedom only. Our results imply that nontrivial induced quantum number on solitons may be a universal feature of spin-charge separation in di erent systems.