Abstract
We study attractive and repulsive screened-two body interactions in the integer quantum Hall effect. Our approach is based on a computation of the fermion determinant associated with the finite-temperature partition function of the system. A Hubbard-Stratonovich transformation on the two-body interaction term is performed, which yields an effective free energy depending on a scalar field. As a result of extremizing the free energy, we find, in the case of repulsive interactions, stable translationally invariant solutions related to integer filling factors of the Landau levels and nontrivial radial solutions, corresponding to excited states that represent depletion of charge in the gas. In the case of attractive interaction, we find nontrivial solutions representing accumulation of charge, with energy lower than the uniform solutions. The true ground state in this case is not given by the uniform solution, opening the possibility of having noninteger filling factors related to a new collective state.
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