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

TL;DR

This paper introduces a geometrically disordered network model for the quantum Hall transition, aligning numerical results with experimental critical exponents and linking the model to quantum gravity, offering new insights into the transition's analytical understanding.

Contribution

The paper develops a generalized network model with geometric disorder, achieving numerical critical exponents consistent with experiments and connecting the model to quenched quantum gravity.

Findings

Numerical critical exponent $ u \\approx 2.37$ matches experimental data.

Geometric disorder maps to Dirac fermions coupled to quantum gravity.

Extends results to other symmetry classes of network models.

Abstract

Recent high-precision results for the critical exponent of the localization length at the integer quantum Hall (IQH) transition differ considerably between experimental ($\nu_\text{exp} \approx 2.38$) 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 a more general network with geometric (structural) disorder. Numerical simulations of this new model lead to the value $\nu \approx 2.37$ in very close agreement with experiments. We argue that in a continuum limit the geometrically disordered model maps to the free Dirac fermion coupled to various random potentials (similar to the CC model) but also to quenched two-dimensional quantum gravity. This explains the possible reason for the considerable difference between critical exponents for the CC model and the geometrically disordered model and may shed more light on the analytical theory of the IQH transition. We extend our results to network models in other symmetry classes.