Complementary colors of colorons: the elementary excitations of the SU(3) Haldane--Shastry model

We propose two possible trial wave functions for the elementary excitations of the SU(3) Haldane--Shastry model, but then argue on very general grounds that only one or the other can be a valid excitation. We then prove explicitly that the trial wave function describing a coloron excitation which transforms according to representation $\bar{3}$ under SU(3) rotations if the spins of the original model transform according to representation 3, is exact. If a basis for the spins on the chain is spanned by the colors blue, red, and green, a basis for the coloron excitations is hence given by the complementary colors yellow, cyan, and magenta. We obtain the dispersion and the exclusion statistics among polarized colorons. Furthermore, we compare our results with the asymptotic Bethe Ansatz and discuss the generalization to SU($n$)

Generic Wavefunction Description of Fractional Quantum Anomalous Hall States and Fractional Topological Insulators

We propose a systematical approach to construct generic fractional quantum anomalous Hall (FQAH) states, which are generalizations of the fractional quantum Hall states to lattice models with zero net magnetic field and full lattice translation symmetry. Local and translationally invariant Hamiltonians can also be constructed, for which the proposed states are unique ground states. Our result demonstrates that generic chiral topologically ordered states can be realized in lattice models, without requiring magnetic translation symmetry and Landau level structure. We further generalize our approach to the time-reversal invariant analog of fractional quantum Hall states--fractional topological insulators, and provide the first explicit wavefunction description of fractional topological insulators in the absence of spin conservation.Comment: 4.5 pages, 2 figure

Non-Abelian Statistics in one dimension: topological momentum spacings and SU(2) level kk fusion rules

We use a family of critical spin chain models discovered recently by one of us [M. Greiter, Mapping of Parent Hamiltonians, Springer, Berlin/Heidelberg 2011] to propose and elaborate that non-Abelian, SU(2) level $k=2S$ anyon statistics manifests itself in one dimension through topological selection rules for fractional shifts in the spacings of linear momenta, which yield an internal Hilbert space of, in the thermodynamic limit degenerate states. These shifts constitute the equivalent to the fractional shifts in the relative angular momenta of anyons in two dimensions. We derive the rules first for Ising anyons, and then generalize them to SU(2) level $k$ anyons. We establish a one-to-one correspondence between the topological choices for the momentum spacings and the fusion rules of spin \half spinons in the SU(2) level $k$ Wess--Zumino--Witten model, where the internal Hilbert space is spanned by the manifold of allowed fusion trees in the Bratelli diagrams. Finally, we show that the choices in the fusion trees may be interpreted as the choices between different domain walls between the $2S+1$ possible, degenerate dimer configurations of the spin $S$ chains at the multicritical point.Comment: 18 pages, 11 figure

The effects of non-abelian statistics on two-terminal shot noise in a quantum Hall liquid in the Pfaffian state

We study non-equilibrium noise in the tunnelling current between the edges of a quantum Hall liquid in the Pfaffian state, which is a strong candidate for the plateau at $\nu=5/2$. To first non-vanishing order in perturbation theory (in the tunneling amplitude) we find that one can extract the value of the fractional charge of the tunnelling quasiparticles. We note however that no direct information about non-abelian statistics can be retrieved at this level. If we go to higher-order in the perturbative calculation of the non-equilibrium shot noise, we find effects due to non-Abelian statistics. They are subtle, but eventually may have an experimental signature on the frequency dependent shot noise. We suggest how multi-terminal noise measurements might yield a more dramatic signature of non-Abelian statistics and develop some of the relevant formalism.Comment: 13 pages, 8 figures, a few change

A family of spin-S chain representations of SU(2)_k Wess-Zumino-Witten models

We investigate a family of spin-S chain Hamiltonians recently introduced by one of us. For S=1/2, it corresponds to the Haldane-Shastry model. For general spin S, we find indication that the low-energy theory of these spin chains is described by the SU(2)_k Wess-Zumino-Witten model with coupling k=2S. In particular, we investigate the S=1 model whose ground state is given by a Pfaffian for even number of sites N. We reconcile aspects of the spectrum of the Hamiltonian for arbitrary N with trial states obtained by Schwinger projection of two Haldane-Shastry chains.Comment: 4.3 pages, 4 figure

Spinon confinement and the Haldane gap in SU(n) spin chains

We use extensive DMRG calculations to show that a classification of SU(n) spin chains with regard to the existence of spinon confinement and hence a Haldane gap obtained previously for valence bond solid models applies to SU(n) Heisenberg chains as well. In particular, we observe spinon confinement due to a next-nearest neighbor interaction in the SU(4) representation 10 spin chain.Comment: 4 pages, 3 figure

Exact models for trimerization and tetramerization in spin chains

We present exact models for an antiferromagnetic S=1 spin chain describing trimerization as well as for an antiferromagnetic S=3/2 spin chain describing tetramerization. These models can be seen as generalizations of the Majumdar-Ghosh model. For both models, we provide a local Hamiltonian and its exact three- or four-fold degenerate ground state wavefunctions, respectively. We numerically confirm the validity of both models using exact diagonalization and discuss the low lying excitations.Comment: 7 pages, 8 figure

Investigations of Pairing in Anyon Systems

We investigate pairing instabilities in the Fermi-liquid-like state of a single species of anyons. We describe the anyons as Fermions interacting with a Chern-Simons gauge field and consider the weak coupling limit where their statistics approaches that of Fermions. We show that, within the conventional BCS approach, due to induced repulsive Coulomb and current-current interactions, the attractive Aharonov-Bohm interaction is not sufficient to generate a gap in the Fermion spectrum.Comment: (11 pages, 2 Figures not included