Geometrically disordered network models, quenched quantum gravity, and critical behavior at quantum Hall plateau transitions

摘要

Recent high-precision results for the critical exponent of the localizationlength at the integer quantum Hall (IQH) transition differ considerably betweenexperimental ($\nu_\text{exp} \approx 2.38$) and numerical ($\nu_\text{CC}\approx 2.6$) values obtained in simulations of the Chalker-Coddington (CC)network model. We revisit the arguments leading to the CC model and consider amore general network with geometric (structural) disorder. Numericalsimulations of this new model lead to the value $\nu \approx 2.37$ in veryclose agreement with experiments. We argue that in a continuum limit thegeometrically disordered model maps to the free Dirac fermion coupled tovarious random potentials (similar to the CC model) but also to quenchedtwo-dimensional quantum gravity. This explains the possible reason for theconsiderable difference between critical exponents for the CC model and thegeometrically disordered model and may shed more light on the analytical theoryof the IQH transition. We extend our results to network models in othersymmetry classes.