In this paper, the degenerate ground states of Z2 topological order on a plane with holes (the so-called surface codes) are used as the protected code subspace to build a topological quantum computer by tuning their quantum tunneling e ect. Using a designer Hamiltonian-the Kitaev toric-code model as an example, we study quantum tunneling e ects of the surface codes and obtain its e ective theory. Finally, we show how to do topological quantum computation including the initialization, the unitary transformation and the measurement.

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 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.

In this paper we systematically study a simple class of translation-symmetry protected topological orders in quantum spin systems using slave-particle approach. The lattice spin systems are translation invariant, but may break any other symmetries. We consider topologically ordered ground states that do not spontaneously break any symmetry. Those states can be described by Z2A or Z2B projective symmetry group. We find that the Z2A translation symmetric topological orders can still be divided into 16 subclasses corresponding to 16 translationsymmetry protected topological orders. We introduced four Z2 topological indices k=0,1 at k=(0,0), (0,π),(π,0), and(π,π) to characterize those 16 topological orders on square lattice. We calculated the topological degeneracies and crystal momenta for those 16 topological phases on even-by-even, even-by-odd, odd-byeven, and odd-by-odd lattices, which allows us to physically measure such topological orders. We predict the appearance of gapless fermionic excitations at the quantum phase transitions between those symmetry protected topological orders. Our result can be generalized to any dimensions. We find 256 translation-symmetry protected Z2A topological orders for a system on three-dimensional cubic lattice.

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, 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.