Classification of quantum Hall universality classes byW1+∞symmetry

1993/10/27 by Andrea Cappelli, A. Cappelli, Carlo A. Trugenberger +3
Materials Science · Physics and Astronomy · #Graphene research and applications #Quantum and electron transport phenomena #Topological Materials and Phenomena #cond-mat #hep-th

paper · pdf · doi:10.1103/physrevlett.72.1902

published as Phys.Rev.Lett. 72 (1994) 1902-1905 · 11 pages, RevTeX 3.0, MPI-Ph/93-75 DFTT 65/93

arxiv created 1993/10/27 · openalex publication_date 1994/03/21 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/31

Abstract

We show how two-dimensional incompressible quantum fluids and their excitations can be viewed as W_1+\mathrm\ensuremath∞ edge conformal field theories, thereby providing an algebraic characterization of incompressibility. The Kac-Radul representation theory of the W_1+\mathrm\ensuremath∞ algebra leads then to a purely algebraic complete classification of hierarchical quantum Hall states, which encompasses all measured fractions. Spin-polarized electrons in single-layer devices can only have Abelian anyon excitations.

Citations

• Conformal symmetry and universal properties of quantum Hall states
• THEORY OF THE EDGE STATES IN FRACTIONAL QUANTUM HALL EFFECTS
• Large N limit in the quantum Hall effect
• W INFINITY AND STRING THEORY