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Besides the conventional bosons and fermions, in synthetic two-dimensional (2D) materials there could exist more exotic quasiparticles with non-Abelian statistics, meaning that the quantum states in the system will be transformed by noncommuting unitary operators when we adiabatically braid the particles one around another. Here, we propose an experimental scheme to observe non-Abelian statistics with cold atoms in a 2D optical lattice. We show that the Majorana-Schockley modes associated with line defects can be braided with non-Abelian statistics through adiabatic shift of the local potentials. We also demonstrate that the braiding operations are robust against typical experimental imperfections and the readout of topological qubits can be accomplished by local measurement of the atom number. [ABSTRACT FROM AUTHOR]

We investigate string correlations in an infinite-size spin-1/2 bond-alternating Heisenberg chain. By employing the infinite matrix product state representation with the infinite time evolving block decimation method, a finite string correlation for extremely large lattice distances is directly observed, in contrast to an extrapolated extreme value for finite size chains. We find that a topological quantum phase transition occurs between two different phases separated and characterized by two different long-range string orders in the space of bond-alternating interactions. Also, the critical exponent ß from the long-range string orders is obtained as ß = 1/12 and the central charge at the critical point is obtained as c ≃ 1, which shows that the topological phase transition belongs to the Gaussian universality class. In addition, it is shown that, for the topological quantum phase transition, the phase boundary can be captured by the singular behavior of the von Neumann entropy and the pinch point of the fidelity per site. [ABSTRACT FROM AUTHOR]