PhD thesis proposed by Hubert SALEUR & Jesper JACOBSEN (LPTENS)
The study of quantum systems in the presence of disorder plays a paramount role in modern condensed matter and statistical physics. Within this realm the Quantum Hall Effect (QHE), which describes the localization and transport properties of a electron gas within an ultra-thin sample of material comprising impurities, is of central importance. After the initial discoveries in the early 1980's of the Integer QHE (IQHE) and the Fractional QHE (FQHE), several variants of the QHE have been considered and classified, among which the Spin Quantum Hall Effect (SQHE) in semiconductors, for which the spin current, rather than the charge current, is quantized.
The main purpose of this PhD is to study the localization/delocalization transition between plateaux in the IQHE using the tools of integrability and conformal field theory. More specifically, the problem will be tackled starting from quantum spin chain and loop models formulations, using numerical diagonalizations, Bethe ansatz and representation theory. Results will then be analyzed in the light of recent progress in (logarithmic) conformal field theory, with the ultimate goal of building the full universality class of the IQHE phase transition, or at least furthering our understanding thereof. Additional aspects such as entanglement and transport could also be studied, depending on the student's rate of progress.
The proposed work will be entirely theoretical, and will potentially involve collaborations with colleagues in Germany, the Netherlands and the USA. The work will be rather interdisciplinary, and use concepts of solid state physics, statistical mechanics and quantum field theory.
Contact: ; tel: +33 (0)1 6908 3002.