Spectral Gaps of Quantum Hall Systems with Interactions
| dc.creator | Koma, Tohru | |
| dc.date | 1998-09-17 | |
| dc.date | 1999-12-27 | |
| dc.date.accessioned | 2026-07-07T03:11:32Z | |
| dc.date.available | 2026-07-07T03:11:32Z | |
| dc.description | A two-dimensional quantum Hall system without disorder for a wide class of interactions including any two-body interaction with finite range is studied by using the Lieb-Schultz-Mattis method [{\it Ann. Phys. (N.Y.)} {\bf 16}: 407 (1961)]. The model is defined on an infinitely long strip with a fixed large width, and the Hilbert space is restricted to the lowest $(n_{\rm max}+1)$ Landau levels with a large integer $n_{\rm max}$. We proved that, for a non-integer filling $ν$ of the Landau levels, either (i) there is a symmetry breaking at zero temperature or (ii) there is only one infinite-volume ground state with a gapless excitation. We also proved the following two theorems: (a) If a pure infinite-volume ground state has a non-zero excitation gap for a non-integer filling $ν$, then a translational symmetry breaking occurs at zero temperature. (b) Suppose that there is no non-translationally invariant infinite-volume ground state. Then, if a pure infinite-volume ground state has a non-zero excitation gap, the filling factor $ν$ must be equal to a rational number. Here the ground state is allowed to have a periodic structure which is a consequence of the translational symmetry breaking. We also discuss the relation between our results and the quantized Hall conductance, and phenomenologically explain why odd denominators of filling fractions $ν$ giving the quantized Hall conductance, are favored exclusively. | |
| dc.description | LaTeX, 54 pages, no figures, discussions on periodic potentials and on energy and spatial cutoffs added, typos corrected, accepted for publication in J. Stat. Phys | |
| dc.identifier | https://arxiv.org/abs/cond-mat/9809228 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/9809228 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/28606 | |
| dc.subject | Mesoscale and Nanoscale Physics | |
| dc.subject | Statistical Mechanics | |
| dc.title | Spectral Gaps of Quantum Hall Systems with Interactions | |
| dc.type | text |