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, the quantum phase transition between superfluid state and Mott-insulator state is studied based on an extended Bose-Hubbard model with two-and three-body on-site interactions. By employing the mean-field approximation we find the extension of the insulating 'lobes' and the existence of a fixed point in three dimensional phase space. We investigate the link between experimental parameters and theoretical variables. The possibility to obverse our results through some experimental effects in optically trapped Bose-Einstein Condensates (BEC) is also discussed.

In this paper we study the Macroscopic Quantum Oscillation (MQO) e ect in ferromagnetic single domain magnets with a magnetic field applied along the hard anistropy axis. The level splitting for the ground state, derived with the conventional instanton method, oscillates with the external field and is quenched at some field values. A formula for quantum tunneling at excited levels is also obtained. The existence of topological phase accounts for this kind of oscillation and the corresponding thermodynamical quantities exhibit similar interference e ects which resembles to some extent the electron quantum phase interference induced by gauge potential in the Aharonov- Bohm effect and the-vacuum in Yang-Mills field theory.

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, it is shown how a single stripe and a stripe phase grow from individual holes in the low-doping regime. In an effective low-energy description of the t-J model, i.e., the phase-string model, a hole doped into the spin-ordered phase will induce a dipolar distortion in the background Kou and Weng, Phys. Rev. B 67, 115103 2003. We analyze the hole-dipole configurations with lowest energy under a dipole-dipole interaction and show that these holes tend to arrange themselves into a regular polygon. Such a stable polygon configuration will turn into a stripe as the number of hole dipoles becomes thermodynamically large and eventually a uniform stripe state can be formed, which constitutes an energetically competitive phase at low doping. We also briefly discuss the effect of Zn impurities on individual hole dipoles and stripes.