Gauge Fields in Condensed Matter

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Location, Location, Location… How charge placement can control a self-assembled structure. Discrete symmetries: C,P,T. Perturbatively induced Chern-Simons terms: Fermion loop. Chapter 5 paragraph 5. Haldane's model for a quantum Hall effect without Landau levels: building block of a topological insulator. Graphene and Haldane's model in an external gauge field: the role of the Chern number for the first part see the paper by G. Reading: Ref 10 Paragraph 3, chapters 3. CS theory on a torus: operator relation for Wilson loops and degeneracy of the ground state on a torus.

Edge states of the integer quantum Hall effect, edge excitations of chiral CS theory and of Z2 spin liquids. Reading: see notes by S.

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    Lattice CS theory and spontaneous formation of a chiral-spin liquid state on a lattice. Title: Gauge Fields in Graphene and an analogy with stochastic semi-classical gravity. Abstract: It is well known that planer graphene quasi-particles behave as massless two dimensional Dirac fermions, Which gives the material many of its interesting properties. The presence of crystal defects and thermal fluctuations result in a curved sheet with non-zero gaussian curvature.

    Book Topology Of Gauge Fields And Condensed Matter

    The electronic structure can be studied in this case as a quantum field theory on a curved background. In this talk, I will review the theory of electronic structure of curved graphene and suggest an analogy with stochastic semi-classical gravity for understanding the back-reaction of electronic excitation on the curvature. It is the simplest toy model for topological order with degenerate ground states.

    The energy excitations are anyonic, which can be used to perform fault tolerant quantum computation. Therefore, it was initially proposed as a system that can be considered as a quantum computer. We will present a detailed analysis of toric code model and discuss some promising future directions. Title: Particle-hole symmetry and interaction effects in the Kane-Mele-Hubbard model. Abstract: At half filling, the Kane-Mele-Hubbard model with purely imaginary next-nearest-neighbor hopping is shown to feature a particle-hole symmetry.

    This symmetry results in the absence of charge and spin currents along open edges, and the absence of sign problem in determinant quantum Monte Carlo simulations. Therefore, the interaction effects on a band topological insulator can be studied numerically in a controlled manner. Through studies of the edge as well as the bulk properties of the model, the ground-state phase diagram is determined. Abstract: Quantum systems that are right at the critical point between two ground states, such as a superfluid and a Mott insulator, exhibit a variety of exotic phenomena. We recently added a new discovery to this area by studying an impurity problem in two-dimensional lattice bosons.

    We considered a static impurity—a repulsive center—and defined its charge as the integrated density distortion it creates in the environment.

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