| Автор | Brian P Dolan |
| Дата выпуска | 1999-05-28 |
| dc.description | We explore the consequences of introducing a complex conductivity into the quantum Hall effect. This leads naturally to an action of the modular group on the upper-half complex conductivity plane. Assuming that the action of a certain subgroup, compatible with the law of corresponding states, commutes with the renormalization group flow, we derive many properties of both the integer and fractional quantum Hall effects including: universality; the selection rule |p<sub>1</sub>q<sub>2</sub>-p<sub>2</sub>q<sub>1</sub>| = 1 for transitions between quantum Hall states characterized by filling factors <sub>1</sub> = p<sub>1</sub>/q<sub>1</sub> and <sub>2</sub> = p<sub>2</sub>/q<sub>2</sub>; critical values of the conductivity tensor; and Farey sequences of transitions. Extra assumptions about the form of the renormalization group flow lead to the semicircle rule for transitions between Hall plateaux. |
| Формат | application.pdf |
| Издатель | Institute of Physics Publishing |
| Название | Duality and the modular group in the quantum Hall effect |
| Тип | lett |
| DOI | 10.1088/0305-4470/32/21/101 |
| Print ISSN | 0305-4470 |
| Журнал | Journal of Physics A: Mathematical and General |
| Том | 32 |
| Первая страница | L243 |
| Последняя страница | L248 |
| Аффилиация | Brian P Dolan; Department of Mathematical Physics, National University of Ireland, Maynooth, Republic of Ireland; Dublin Institute for Advanced Studies, 10 Burlington Road, Dublin, Republic of Ireland |
| Выпуск | 21 |
