Many-Body Theory: The Fractional Quantum Hall Effect.

Allan H. MacDonald

Gautam Dev, Jainendra K. Jain

The eigenstates of interacting electrons in the fractional quantum Hall phase typically form fairly well-defined bands in the energy space. We study systems of six and eight electrons for filling factor 3/7>\ensuremath{\nu}> 2) / 7 and show that composite fermion theory gives insight into the origin of these bands and provides an accurate and complete microscopic description of the strongly correlated many-body states in the low-energy bands. This implies that, somewhat like in Landau's Fermi liquid theory, there is a one-to-one analogy between the low-energy Hilbert space of strongly interacting electrons in the fractional quantum Hall effect and that of weakly interacting electrons in the integer quantum Hall effect.

Manas Pratim Das, Jagadishwar Mahanty

Introductory many-body theory, D.J. Thouless collective description of many-body systems, R.M. Dreizler fermi liquid theory, D. Pines theory of fractional quantum hall effect, A.H. MacDonald numerical methods for problems of interacting many electron systems, D.J. Scalapino supersymmetry in nuclear and condensed matter physics, A.B. Balantekin strongly coupled plasmas, K.I. Golden fractional quantum hall effect and electron solid, R.G. Clark models to treat strong electronic correlations, M.P. Das physics of anyons, R.B. Laughlin. (Part contents).

R. Morf

Vladimir A. Zyuzin

In this paper we propose a model of the fractional quantum Hall effect within conventional one-dimensional bosonization. It is shown that in this formalism the resulting bosonized fermion operator corresponding to momenta of Landau gauge wave function is effectively two-dimensional. At special filling factors the bulk gets gapped, and the theory is described by a sine-Gordon model. The edges are shown to be gapless, chiral, and carrying a fractional charge. The hierarchy of obtained fractional charges is consistent with existing experiments and theories. It is also possible to draw a connection to composite fermion description and to the Laughlin many-body wave function.

Jonathan Bain