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.

The properties of a class of topological quantum phase transition (TQPT) are analyzed based on a model proposed by Haldane. We study the effect of finite temperature on this phase transition. We have found that finite temperature would drive this TQPT to be a crossover, while it is stable against the weak short range interaction. When the interaction is strong enough, however, this TQPT is unstable and other states would emerge. Then we investigate the effect of the on-site energy in the original haldane model. The critical di erence between our TQPT and the topological phase transition in conventional quantum Hall system is discussed. Finally, we discuss the potential application of our analysis to a topological phase transition proposed in a realistic system.

Based on an e ective model of a doped antiferromagnetic Mott insulator, we show that a doped hole will induce a dipole-like spin configuration in a spin ordered phase at low doping. The kinetic energy of doped holes is severely frustrated and a hole-dipole object is actually localized or selftrapped in space. Without a balance from the kinetic energy, the long-range dipole-dipole interaction between doped holes will dominate the low-energy physics, leading to an inhomogeneity instability as hole-dipoles collapse into stripes. Both antiphase metallic stripes of quarter-filling and antiphase insulating stripes along a diagonal direction are discussed as composed of hole-dipoles as elementary building blocks. Stripe melting and competing phases are also discussed.

In this paper, we propose a method to understand the nature for the quantum disorder phase of the two-dimensional (2D) high spin frustrated model. The ground state and excitation properties of a fully frustrated 2D spin-1 model are studied based on a model whose groundstate can be found exactly. By analogy to the pseudo-potential approach in the fractional quantum Hall effect, we conclude that the ground states of the fully frustrated spin-1 model are doubly degenerate valance bond solid (VBS) states along the horizontal or vertical direction of the square lattice. We also find that the ground state could be characterized by a nonzero string order, which rarely happened in the 2D case. The method that we used reveals the connection between the fractional quantum hall e ect and the frustrated 2D antiferromagnetism system. The VBS states capture the main character of the disordered phase in the 2D spin-1 frustrated system, and can be verified by a numerical method.

We show that a topological gauge structure in an e ective description of the t-J model gives rise to a global phase diagram of antiferromagnetic (AF) and superconducting (SC) phases in a weakly doped regime. Dual confinement and deconfinement of holons and spinons play essential roles here, with a quantum critical point at a doping concentration xc≃0.043. The complex experimental phase diagram at low doping is well described within such a framework.