We predict the effect of the roton instability for a two-dimensional weakly interacting gas of tilted dipoles in a single homogeneous quantum layer. Being typical for strongly correlated systems, the roton phenomena appear to occur in a weakly interacting gas. It is important that in contrast to a system of normal to the layer dipoles, breaking of the rotational symmetry for a system of tilted dipoles leads to the convergence of the condensate depletion even up to the threshold of the roton instability, with mean-field approach being valid. Predicted effects can be observed in a wide class of dipolar systems. We suggest observing predicted phenomena for systems of ultracold atoms and polar molecules in optical lattices, and estimate optimal experimental parameters.We predict the effect of the roton instability for a two-dimensional weakly interacting gas of tilted dipoles in a single homogeneous quantum layer. Being typical for strongly correlated systems, the roton phenomena appear to occur in a weakly interacting gas. It is important that in contrast to a system of normal to the layer dipoles, breaking of the rotational symmetry for a system of tilted dipoles leads to the convergence of the condensate depletion even up to the threshold of the roton instability, with mean-field approach being valid. Predicted effects can be observed in a wide class of dipolar systems. We suggest observing predicted phenomena for systems of ultracold atoms and polar molecules in optical lattices, and estimate optimal experimental parameters.

arXiv:1407.6399Physical Review AOct 16, 201430 citations

Fractional quantum numbers and electron correlations

W. Gasser

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.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.

Physical review. B, Condensed matterJan 15, 19932 citations

Instabilities of correlated electrons on the honeycomb lattice

Carsten Honerkamp A

Bulletin of the American Physical SocietyMar 8, 20070 citations

Superconducting and density wave instabilities for strongly correlated electrons in two dimensions

Johannes Voit, E. J. Melé

Synthetic MetalsJun 1, 19911 citation

Correlated Disorder in One-dimensional Electronic Systems

Niaz Ali Khan

Jul 30, 20196 citations

{\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.