Exact results for interacting electrons in high Landau levels
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-->∞, 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 Tt. 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.
- Publication:
-
Physical Review B
- Pub Date:
- August 1996
- DOI:
- 10.1103/PhysRevB.54.5006
- arXiv:
- arXiv:cond-mat/9606177
- Bibcode:
- 1996PhRvB..54.5006M
- Keywords:
-
- 71.70.Di;
- 73.20.Dx;
- 73.20.Mf;
- 73.40.Hm;
- Landau levels;
- Collective excitations;
- Condensed Matter
- E-Print:
- RevTex, 12 pages with figures included in same file