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.

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.

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.

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.