Berlin 2015 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 55: Low-Dimensional Systems: 2D – Theory
TT 55.4: Vortrag
Mittwoch, 18. März 2015, 10:15–10:30, H 3010
The spectra of integrable staggered sl(2|1) network models — •Andreas Klümper1 and Michael Brockmann2 — 1Universität Wuppertal, Theoretische Physik, Gauss-Strasse 20, 42119 Wuppertal — 2Institute for Theoretical Physics, University of Amsterdam, Science Park 904, 1090 GL Amsterdam
We investigate the spectra of transfer matrices of integrable Chalker-Coddington like network models with sl(2|1) symmetry and staggered 3−3 representations. Related to these network models are integrable superspin chains. The research on these models is motivated in general by the spin quantum Hall effect.
There are two kinds of integrable staggered sl(2|1) models : (i) a rather well understood system based on the Temperley-Lieb algebra, (ii) a system based on the Hecke algebra and introduced by R. M. Gade in 1998. The latter model satisfies nested Bethe ansatz equations and was investigated extensively and particularly numerically by Essler, Frahm, Saleur in 2005.
We aim at an analytical treatment of the nested Bethe ansatz equations and derive a closed finite set of non-linear integral equations. These equations are well-posed and valid for any system size as well as for the largest and next-largest eigenvalues of the transfer matrix. The numerical treatment is delicate as straight forward iterations do not converge. However, the equations allow for analytical calculations of conformal properties.