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.

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, 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.

The crossover from thermal hopping to quantum tunneling is studied. We show that the decay rate-with dissipation can accurately be determined near the crossover temperature. Besides considering the Wentzel-Kramers-Brillouin (WKB) exponent, we also calculate contribution of the fluctuation modes around the saddle point and give an extended account of a previous study of crossover region. We deal with two dangerous fluctuation modes whose contribution can't be calculated by the steepest descent method and show that higher order couplings between the two dangerous modes need to be taken into considerations. At last the crossover from thermal hopping to quantum tunneling in the molecular agnet Mn12Ac is studied.

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.