Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/0104035

Quantum groups and nonabelian braiding in quantum Hall systems

J. K. Slingerland·F. A. Bais
View original source ↗Read source document ↗Export metadata ↓

Abstract

Wave functions describing quasiholes and electrons in nonabelian quantum Hall states are well known to correspond to conformal blocks of certain coset conformal field theories. In this paper we explicitly analyse the algebraic structure underlying the braiding properties of these conformal blocks. We treat the electrons and the quasihole excitations as localised particles carrying charges related to a quantum group that is determined explicitly for the cases of interest. The quantum group description naturally allows one to analyse the braid group representations carried by the multi-particle wave functions. As an application, we construct the nonabelian braid group representations which govern the exchange of quasiholes in the fractional quantum Hall effect states that have been proposed by N. Read and E. Rezayi, recovering the results of C. Nayak and F. Wilczek for the Pfaffian state as a special case.

Explore related subjects

cond-mat.mes-hallhep-thmath-phmath.MPmath.QA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

J. K. Slingerland, F. A. Bais. 2001-04-02. Quantum groups and nonabelian braiding in quantum Hall systems. https://doi.org/10.1016/s0550-3213(01)00308-x

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Benzo-bis(imidazole) self-assembled monolayers molecular junctions in meta or para conformation: effects of protonation on the electrical and thermal conductances

We report the thermal conductances of molecular junctions made of self-assembled monolayers of benzo-bis(imidazole) molecules, without side groups or functionalized with two phenylamine side groups. In the two cases, when the molecules are connected to the electrodes by thiol anchoring groups in the meta-position, the thermal conductance is decreased compared to the same molecules connected in the para-position (ca. 16-29 nW/K and ca. 37-40 nW/K, respectively) in agreement with the theoretically predicted phonon interference effect in molecular junctions. Upon protonation, the thermal conductances of the meta-connected molecular junction increase by about 50% (reversible behavior upon deprotonation). The fact that only the thermal conductance of the meta-connected molecular junction is sensitive to the protonation/deprotonation is tentatively related to modifications of the structural organization of the molecules in the monolayer, which modifies the thermal conductance at the molecule/electrode interfaces. The electrical conductance is lower for the meta-connected molecule than for the para-connected one, due to destructive quantum interferences, as expected and reported for other molecular junctions. The conductance further decreases (reversibly) upon protonation. The energy position of the molecular orbital involved in the electron transport is not modified by the protonation and the decrease in current is related to changes in the molecule organization in the monolayer, which modulate the electronic coupling energy at the molecule/electrode interfaces.

cond-mat.mes-hall↗
arXiv2026

Hydrodynamics of two-dimensional electrons due to scattering by disorder

The hydrodynamic regime of electron transport, induced by fast inter-electron collisions, was discovered in high-quality nanostructures in recent ten years. However, signs of hydrodynamic transport, primarily, the giant negative magnetoresistance, were observed even at very low temperatures, when electron-electron scattering is too weak to affect the transport. To address this puzzle, here we develop a theory of mixed, hydrodynamic and non-Markovian, magnetotransport of two-dimensional electrons at zero temperature in samples with weak but still important disorder. Namely, we account for both the memory effects at electron scattering by localized defects in magnetic field and an unconventional viscosity effect due to electron scattering by defects in bulk and by rough sample edges. Solution of the model yields a strong negative magnetoresistance, which exhibits at zero magnetic field a sharp maximum in narrower samples or a blunt maximum in wider samples. This and other our results explain various properties of the giant negative magnetoresistance observed on ultra-high-quality GaAs quantum wells, thereby we apparently reveal the nature of low-temperature magnetotransport in these systems.

cond-mat.mes-hall↗
arXiv2026

Symplectic Hopf Insulator: Delicate Topology in Bosonic Bogoliubov-de Gennes Systems

Recent advances in topological phases have highlighted the role of symplectic (Krein-space) topology in the classification of bosonic Bogoliubov-de Gennes (BBdG) systems. In this work, we construct a BBdG realization of Hopf topology, which we dub the symplectic Hopf insulator, starting from a microscopic Bose-Hubbard generalization of the Moore-Ran-Wen model with weak on-site interactions treated within a Bogoliubov approximation. The resulting BBdG system admits a symplectic Hopf invariant, which we show to be integer-quantized for isolated bands. We establish that this topology is intrinsically delicate, requiring exactly two bosonic modes per unit cell, while remaining robust against weak interactions over a range of mass parameters. Upon terminating the three-dimensional insulator at a boundary, we find topologically protected in-gap surface states at finite excitation energy, whose protection is itself delicate. Our results establish the symplectic Hopf insulator as a robust yet delicate topological phase in weakly interacting bosonic systems lying beyond the tenfold-way classification.

cond-mat.mes-hall↗