Exact results for interacting electrons in high Landau levels

Details Exact results for interacting electrons in high Landau levels Exact results for interacting electrons in high Landau levels

1996-06-24

arxiv.org/abs/cond-mat/9606177v1

Phys. Rev. B 54, 5006 (1996)

Physics

Condensed Matter

RevTex, 12 pages with figures included in same file; to appear in Physical Review B

Scientific paper

10.1103/PhysRevB.54.5006

We study a two-dimensional electron system in a magnetic field with a fermion hardcore interaction and without disorder. Projecting the Hamiltonian onto the n-th Landau level, we show that the Hartree-Fock theory is exact in the limit n \rightarrow \infty, 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.

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