Ground-state energy of two-dimensional interacting electrons in strong magnetic fields

G. Meissner, U. Brockstieger

Y. F Ge

The Schrödinger equation for the two-body problem of two-dimensional interacting electrons in a magnetic field is exactly solved. It is found that the degeneracy of the Landau levels for noninteracting electrons is removed by the Coulomb interaction, and that the ground state is nondegenerate and possesses an energy gap from the first excited state. Our result suggests that the interacting electrons in a strong magnetic field form a new condensate which may be identified as a vortex.

No author provided

The ground-state energy of two-dimensional interacting electrons in a strong magnetic field in the angular-momentum representation is studied using a modified Lanczos diagonalization method. In the presence of a positive background density the ground-state energy increases with the total angular momentum, while a cusp-type behaviour appears. The problem of the electron-impurities interaction is formulated as well. The results are discussed in connection with the observed fractional quantum Hall states.

Veikko Halonen

P. Schlottmann, Rolf R. Gerhardts

D. Ninno, Giuseppe Iadonisi

Energy levels of two-dimensional Fr\"ohlich polarons in a magnetic field are calculated variationally by use of a generalization of the Lee-Low-Pines ansatz for the variational wave function allowing the phonon distribution function to depend on the electronic coordinates. It is shown that this choice leads to the correct interpolation between the weak- and strong-field limits. Comparing our ground-state energies with those obtained within second-order perturbation theory and the path-integral method, we argue that neither of these methods gives a satisfactory description of the dynamics of the electron-phonon interaction under the influence of an external field.