Exact results for interacting electrons in high Landau levels

1996/06/24 by Roderich Moessner, R. Moessner, J. T. Chalker · 16 citations
Materials Science · Physics and Astronomy · #Organic and Molecular Conductors Research #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #cond-mat

paper · pdf · doi:10.1103/physrevb.54.5006

published as Phys. Rev. B 54, 5006 (1996) · RevTex, 12 pages with figures included in same file; to appear in Physical Review B

arxiv created 1996/06/24 · openalex publication_date 1996/08/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study a two-dimensional electron system in a magnetic field with a fermion hard-core interaction and without disorder. Projecting the Hamiltonian onto the nth Landau level, we show that the Hartree-Fock theory is exact in the limit n\ensuremath→\ensuremath∞, for the high-temperature, uniform density phase of an infinite system; for a finite-size system, it is exact at all temperatures. In addition, we show that a charge-density wave arises below a transition temperature T_t. Using Landau theory, we construct a phase diagram which contains both unidirectional and triangular charge-density wave phases. We discuss the unidirectional charge-density wave at zero temperature and argue that quantum fluctuations are unimportant in the large-n limit. Finally, we discuss the accuracy of the Hartree-Fock approximation for potentials with a nonzero range such as the Coulomb interaction. \textcopyright 1996 The American Physical Society.

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