$W_{1+\infty}$ Dynamics of Edge Excitations in the Quantum Hall Effect

Details $W_{1+\infty}$ Dynamics of Edge Excitations in the Quantum Hall Effect $W_{1+\infty}$ Dynamics of Edge Excitations in the Quantum Hall Effect

1994-07-23

arxiv.org/abs/cond-mat/9407095v1

Annals Phys. 246 (1996) 86-120

Physics

Condensed Matter

TeX file (needs harvmac), 39 pages, preprint MPI-PhT/94-35 and DFTT-16/94

Scientific paper

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.

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