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In this paper, to characterize the effect of topological defects on the entanglement of topological states, we introduce the concept of local entanglement entropy. By using the spinless p x + i p y superconductor with quantized vortices, we numerically calculated the local entanglement entropy. In the topological superconducting (weak-pairing) phase, we found that the local entanglement entropy turns to 0.5 for a Majorana zero mode. For the system with two/four Majorana zero modes, by calculating local entanglement entropy, we found the non-locality effect of Majorana zero modes. In the future, we will use local entanglement entropy to characterize the defect effect on other many-body systems with long entanglement, for example, topological order and quantum spin liquid. [ABSTRACT FROM AUTHOR]

In this paper, starting from Biot-Savart mechanics for entangled vortex-membranes, a new theory - knot physics - is developed to explore the underlying physics of quantum mechanics. Owning to the conservation conditions of the volume of knots on vortices in incompressible fluid, the shape of knots will never be changed and the corresponding Kelvin waves cannot evolve smoothly. Instead, the knot can only be split. The knot-pieces evolve following the equation of motion of Biot-Savart equation that becomes Schrödinger equation for probability waves of knots. The classical functions for Kelvin waves become wave-functions for knots. The effective theory of perturbative entangled vortex-membranes becomes a traditional model of relativistic quantum field theory - a massive Dirac model. As a result, this work would help researchers to understand the mystery in quantum mechanics. [ABSTRACT FROM AUTHOR]

In this paper, we numerically study the non-Abelian statistics of the zero-energy Majorana fermions at the end of Majorana chain and show its application to quantum computing by mapping it to a spin model with special symmetry. In particular, by using transverse-field Ising model with Z2 symmetry, we verify the nontrivial non-Abelian statistics of Majorana fermions. Numerical evidence and comparison in both Majorana representation and spin representation are presented. The degenerate ground states of a symmetry protected spin chain therefore provide a promising platform for topological quantum computation. [ABSTRACT FROM AUTHOR]

Recently, Majorana fermions (MFs) have attracted intensive attention due to their exotic statistics and possible applications in topological quantum computation. They are proposed to exist in various two-dimensional (2D) topological systems, such as topological superconductor (SC) and nanowire-superconducting hybridization system. In this paper, we point out that Majorana fermions in different topological systems obey different types of polygon sign rules. A numerical approach is described to identify the type of polygon sign rule of the Majorana fermions. Applying the approach to study two 2D topological systems, we find that vortex-induced Majorana fermions obey topological polygon sign rule and line-defect-induced Majorana fermions obey normal polygon sign rule. [ABSTRACT FROM AUTHOR]

We propose a possible way, theoretically, to manipulate a Schrödinger cat state of two degenerate ferromagnetic [FM] ground states of the transverse Ising model [TIM] using macroscopic quantum tunneling (MQT) effect. The MQT process is calculated based on a high-order degenerate perturbative method and can be understood in the language of individual virtual fermions hopping along the spin chain. We present an analytical description of the tunneling process, and discuss experimental feasibility for generating the Cat state in the linear ion trap. [ABSTRACT FROM AUTHOR]

In this paper, we studied a generalized Bose-Hubbard model on a checkerboard lattice with topologically nontrivial flat-band. We used mean-field method to decouple the model Hamiltonian and obtained phase diagram by Landau theory of second-order phase transition. We further calculate the energy gap and the dispersion of quasi-particle or quasi-hole in Mott insulator phase and found that in strong interaction limit the quasi-particles or the quasi-holes also have flat-bands. [ABSTRACT FROM AUTHOR]

In this paper, starting from a lattice model of topological insulators, we study the quantum phase transitions among different quantum states, including quantum spin Hall state, quantum anomalous Hall state and normal band insulator state by calculating their topological properties (edge states, quantized spin Hall conductivities, and the number of zero mode on a π-flux). We find that at the topological quantum phase transitions (TQPTs), the topological "order parameter" - spin Chern number will jump. And since the masses of the nodal fermions will change sign, the third derivative of ground-state energy is nonanalytic. In addition, we discuss the finite temperature properties and the stability of the TQPTs. [ABSTRACT FROM AUTHOR]

In this paper, we systematically analyze the properties of the bosonic t-J model simulated in optical superlattices. In particular, by using a slave-particle approach, we show the emergence of a strange topological Fermi liquid with Fermi surfaces from a purely bosonic system. We also discuss the possibility of observing these phenomena in ultracold atom experiments. The result may provide some crucial insights into the origin of high-Tc superconductivity. [ABSTRACT FROM AUTHOR]

In this paper it is shown that the gauge fixing term is not only gauge fixing term in D dimensions, but also the mass term for gauge field in (D+2)-dimensional superspace [or (D-2)-dimensional space], more importantly the kinetic term for the gauge modes g(x) is the so-called (D-2)-dimensional SU(N)×SU(N) principal chiral model. The results conform Migdal's scheme about the connection between four-dimensional gauge field and two-dimensional chiral system. And the recursion relation can be generalized to D dimensions gauge theories with chiral models in D-2 dimensions. With the new local order parameter for Yang–Mills field |[sub D-2], the results are consistent with lattice results qualitatively: there is no phase transition in low dimensions (D≤4), while in higher dimensions first-order phase transition appears between strong coupling region and weak coupling region. [ABSTRACT FROM AUTHOR]