Condensed Matter Theory

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.

Abstract:

We study the static properties of cubic blue phases by numerically minimizing the three-dimensional, Landau-de Gennes free energy for a cholesteric liquid crystal close to the isotropic-cholesteric phase transition. Thus we are able to refine the powerful but approximate, semianalytic frameworks that have been used previously. We obtain the equilibrium phase diagram and discuss it in relation to previous results. We find that the value of the chirality above which blue phases appear is shifted by 20% (toward experimentally more accessible regions) with respect to previous estimates. We also find that the region of stability of the O5 structure-which has not been observed experimentally-shrinks, while that of blue phase I ( O-8 ) increases thus giving the correct order of appearance of blue phases at small chirality. We also study the approach to equilibrium starting from the infinite chirality solutions and we find that in some cases the disclination network has to assemble during the equilibration. In these situations disclinations are formed via the merging of isolated aligned defects.