Fractional quantum numbers and electron correlations.

Abstract

It will be shown that sequences of fractional quantum numbers (in this case occupation numbers) appear to be important for the instabilities of a one-dimensional Hubbard model in the strong-correlation limit (\ensuremath{\Delta}/U\ensuremath{\ll}1, but finite) if only the highest commensurability is observed and besides the 2${\mathit{k}}_{\mathit{F}}$ instability the 2${\mathit{lk}}_{\mathit{F}}$ instabilities are also taken into consideration. These sequences obey an odd-denominator rule. Further, it will be shown that an interacting two-dimensional electron gas in a strong external magnetic field and under the influence of a weak sinusoidal substrate potential may be described by a one-dimensional Hubbard model which also gives fractional quantum numbers (in this case fractional filling factors) again exhibiting an odd-denominator rule.