Exact results for interacting electrons in high Landau levels

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.