The Chalker-Coddington Network Model is Quantum Critical

TL;DR

This paper demonstrates that the localization transition in the integer quantum Hall effect, modeled by the Chalker-Coddington network, exhibits quantum criticality, confirmed through numerical and analytical methods.

Contribution

It maps the network model to a non-Hermitian supersymmetric Hamiltonian and proves quantum criticality at the transition.

Findings

Critical behavior observed at the plateau transition

Numerical analysis confirms quantum criticality

Analytic proof via generalized Lieb-Schultz-Mattis theorem

Abstract

We show that the localization transition in the integer quantum Hall effect as described by the Chalker-Coddington network model is quantum critical. We first map the anisotropic network model to the problem of diagonalizing a one-dimensional non-Hermitian non-compact supersymmetric lattice Hamiltonian of interacting bosons and fermions. Its behavior is investigated numerically using the density matrix renormalization group method, and critical behavior is found at the plateau transition. This result is confirmed by an exact, analytic, generalization of the Lieb-Schultz-Mattis theorem.