Abelian and non-Abelian statistics in the coherent state representation

We further develop an approach to identify the braiding statistics associated to a given fractional quantum Hall state through adiabatic transport of quasiparticles. This approach is based on the notion of adiabatic continuity between quantum Hall states on the torus and simple product states---or "patterns"---in the thin torus limit, together with a suitable coherent state Ansatz for localized quasiholes that respects the modular invariance of the torus. We give a refined and unified account of the application of this method to the Laughlin and Moore-Read states, which may serve as a pedagogical introduction to the nuts and bolts of this technique. Our main result is that the approach is also applicable---without further assumptions---to more complicated non-Abelian states. We demonstrate this in great detail for the level $k=3$ Read-Rezayi state at filling factor $\nu=3/2$. These results may serve as an independent check of other techniques, where the statistics are inferred from conformal block monodromies. Our approach has the benefit of giving rise to intuitive pictures representing the transformation of topological sectors during braiding, and allows for a self-consistent derivation of non-Abelian statistics without heavy mathematical machinery.Comment: 38 pages, 11 figures, REVTeX 4-1; grammar and typo fixes, published versio

Momentum resolved tunneling into the Pfaffian and anti-Pfaffian edges

We calculate the electron spectral functions at the edges of the Moore-Read Pfaffian and anti-Pfaffian fractional quantum Hall states, in the clean limit. We show that their qualitative differences can be probed using momentum resolved tunneling, thus providing a method to unambiguously distinguish which one is realized in the fractional quantum Hall state observed at filling factor $\nu=5/2$. We further argue that edge reconstruction, which may be less important in the first excited Landau level (LL) than in the lowest LL, can also be detected this way if present.Comment: published versio

Domain wall type defects as anyons in phase space

We discuss how the braiding properties of Laughlin quasi-particles in quantum Hall states can be understood within a one-dimensional formalism we proposed earlier. In this formalism the two-dimensional space of the Hall liquid is identified with the phase space of a one-dimensional lattice system, and localized Laughlin quasi-holes can be understood as coherent states of lattice solitons. The formalism makes comparatively little use of the detailed structure of Laughlin wavefunctions, and may offer ways to be generalized to non-abelian states.Comment: published versio

Bounds for low-energy spectral properties of center-of-mass conserving positive two-body interactions

We study the low-energy spectral properties of positive center-of-mass conserving two-body Hamiltonians as they arise in models of fractional quantum Hall states. Starting from the observation that positive many-body Hamiltonians must have ground-state energies that increase monotonously in particle number, we explore what general additional constraints can be obtained for two-body interactions with "center-of-mass conservation" symmetry, both in the presence and absence of particle-hole symmetry. We find general bounds that constrain the evolution of the ground-state energy with particle number, and in particular, constrain the chemical potential at $T=0$. Special attention is given to Hamiltonians with zero modes, in which case similar bounds on the first excited state are also obtained, using a duality property. In this case, in particular, an upper bound on the charge gap is also obtained. We further comment on center of mass and relative decomposition in disk geometry within the framework of second quantization.Comment: 8 pages, published versio