W(1+infinity) dynamics of edge excitations in the quantum Hall effect

A. CAPPELLI, C. A TRUGENBERGER , G. R. ZEMBA

ANNALS OF PHYSICS (NEW YORK)

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: New York, EEUU; Año: 1996 vol. 246 p. 86 - 120

0003-4916

Quantum Hall universality classes can be classified by $W_{1+infty}$ symmetry. We show that this symmetry also governs the dynamics of quantum edge excitations. The Hamiltonian of interacting electrons in the fully-filled first Landau level is expressed in terms of $W_{1+infty}$ generators. The spectra for both the Coulomb and generic short-range interactions are thus found algebraically. We prove the one-dimensional bosonization of edge excitations in the limit of large number of particles. Moreover, the subleading corrections are given by the higher-spin $W_{1+infty}$ generators, which measure the radial fluctuations of the electron density. The resulting spectrum for the Coulomb interaction contains a logarithmic enhancement, in agreement with experimental observations. The spectrum for generic short-range interactions is subleading and reproduces the classical capillary frequencies. These results are also extended to fractional filling by using symmetry arguments.