An integrable model for the integer quantum Hall transition I: The vertex model

TL;DR

This paper introduces an integrable vertex model based on quantum affine superalgebra to describe the integer quantum Hall transition, providing a new mathematical framework for understanding this quantum phase transition.

Contribution

The paper constructs a novel integrable vertex model using quantum affine superalgebra, linking it to the super spin chain Hamiltonian relevant for the quantum Hall transition.

Findings

Model characterized by specific spectral parameters and modules

Solutions yield Boltzmann weights for the vertex model

Contains a conserved charge equivalent to the super spin chain Hamiltonian

Abstract

In this study, an integrable vertex model based on the quantum affine superalgebra $U_q\bigl(\hat{gl}(2|2)\bigr)$ is constructed. The model is characterized by a particular assignment of spectral parameters and lowest as well as highest weight $U_q\bigl(gl(2|2) \bigr)$ modules to its lattice links. Solutions of the corresponding intertwining conditions yield the Boltzmann weights. The set of mutually commuting charges contains a quantity equivalent to the super spin chain Hamiltonian proposed for the description of the integer quantum Hall transition.