EXACT RESULTS FOR INTERACTING ELECTRONS IN HIGH LANDAU-LEVELS

We study a two-dimensional electron system in a magnetic field with a fermion hard-core interaction and without disorder. Projecting the Ham iltonian onto the nth Landau level, we show that the Hartree-Fock theo ry is exact in the limit n-->infinity, for the high-temperature, unifo rm density phase of an infinite system; for a finite-size system, it i s exact at all temperatures. In addition, we show that a charge-densit y wave arises below a transition temperature T-t. Using Landau theory, we construct a phase diagram which contains both unidirectional and t riangular charge-density wave phases. We discuss the unidirectional ch arge-density wave at zero temperature and argue that quantum fluctuati ons are unimportant in the large-n limit. Finally, we discuss the accu racy of the Hartree-Fock approximation for potentials with a nonzero r ange such as the Coulomb interaction.