Related papers: Fibonacci topological order from quantum nets
A new topological field theory is constructed, which is characterized by cubic interactions similar to those of non-abelian Chern-Simons field theories, but still retains the simplicity of the abelian case. The perturbative expansion of…
Periodic Hamiltonians on a three-dimensional (3-D) lattice with a spectral gap not only on the bulk but also on two edges at the common Fermi level are considered. By using K-theory applied for the quarter-plane Toeplitz extension, two…
The spectrum of spinless, non-interacting electrons on a linear chain that is buckled in a non- uniform manner giving it a flavor of a topologically disordered lattice, is investigated within a tight binding formalism. We have addressed two…
A topological quantum field theory of non-abelian differential forms is investigated from the point of view of its possible applications to description of polynomial invariants of higher-dimensional two-component links. A path-integral…
In the past few years, we have presented a new way of considering quark confinement. Through a careful choice of a Cho-Duan-Ge Abelian Decomposition, we can construct the QCD Wilson Loop in terms of an Abelian restricted field. The…
A realistic material may possess defects, which often bring the material new properties that have practical applications. The boundary defects of a two-dimensional topologically ordered system are thought of as an alternative way of…
Knots have a twisted history in quantum physics. They were abandoned as failed models of atoms. Only much later was the connection between knot invariants and Wilson loops in topological quantum field theory discovered. Here we show that…
Entanglement is a special feature of the quantum world that reflects the existence of subtle, often non-local, correlations between local degrees of freedom. In topological theories such non-local correlations can be given a very intuitive…
We show that the edge states of the four-dimensional class A system can have topological charges, which are characterized by Abelian/non-Abelian monopoles. The edge topological charges are a new feature of relations among theories with…
The search for exotic new topological states of matter in widely accessible materials, for which the manufacturing process is mastered, is one of the major challenges of the current topological physics. Here we predict higher order…
We establish an important duality correspondence between topological order in quantum many body systems and criticality in ferromagnetic classical spin systems. We show how such a correspondence leads to a classical and simple procedure for…
We describe topologically ordered and fracton ordered states on novel geometries which do not have an underlying manifold structure. Using tree graphs such as the $k$-coordinated Bethe lattice ${\cal B}(k)$ and a hypertree called the…
A large class of topological orders can be understood and classified using the string-net condensation picture. These topological orders can be characterized by a set of data (N, d_i, F^{ijk}_{lmn}, \delta_{ijk}). We describe a way to…
Competing interactions in quantum magnets lead to a variety of emergent states, including ordered phases, nematic magnets and quantum spin liquids. Among them, topological quantum magnets represent a promising platform to create topological…
We show that chains of interacting Fibonacci anyons can support a wide variety of collective ground states ranging from extended critical, gapless phases to gapped phases with ground-state degeneracy and quasiparticle excitations. In…
Determining the statistics of elementary excitations supported by fractional quantum Hall states is crucial to understanding their properties and potential applications. In this paper, we use the topological entanglement entropy as an…
Two-dimensional systems such as quantum spin liquids or fractional quantum Hall systems exhibit anyonic excitations that possess more general statistics than bosons or fermions. This exotic statistics makes it challenging to solve even a…
Topological order has proven a useful concept to describe quantum phase transitions which are not captured by the Ginzburg-Landau type of symmetry-breaking order. However, lacking a local order parameter, topological order is hard to…
Topological concepts have been employed to understand the ground states of many strongly correlated systems, but it is still quite unclear if and how topology manifests itself in the relaxation dynamics. Here we uncover emergent topological…
Non-Abelian anyons promise to reveal spectacular features of quantum mechanics that could ultimately provide the foundation for a decoherence-free quantum computer. A key breakthrough in the pursuit of these exotic particles originated from…