Professor Fabian Essler

Abstract:

The analysis of network models - either directly or by numerical studies of related quantum spin chains with super group symmetry - allows to gain insights into the delocalization transition of non-interacting two-dimensional electrons with disorder. Critical exponents determined this way are an important step towards the identification of the conformal field theory (CFT) describing the universal physics at the transition. To collect more information on the universal properties integrable versions of the corresponding superspin chains have been proposed. A simplified version avoiding some of the technical problems of the original problem is the sl(2|l) superspin chain related to the so-called spin quantum Hall transition. Analyzing the ground state and some low-lying excitations of this integrable chain we determine the central charge of the underlying CFT and obtain evidence for an infinite degeneracy of the finite size gaps that are possibly related to a continuous spectrum of the CFT. Finally, we compare our findings for the integrable chain with known properties of the (non-integrable) network model for the spin QHE. © Springer-Verlag Berlin Heidelberg 2005.