Hidden Massive Spectators in the Effective Field Theory for Integral Quantum Hall Transitions

TL;DR

This paper develops an effective field theory for integer quantum Hall transitions that incorporates massive spectator Dirac fermions to accurately reproduce topological invariants and conductance changes.

Contribution

It introduces a method to identify massive spectator fermions in the effective theory based on microscopic vortex information, enhancing understanding of quantum Hall transitions.

Findings

Correctly reproduces Hall conductance values before and after transitions.

Provides a general prescription for determining spectator fermions from microscopic data.

Demonstrates the approach in a lattice model with various hoppings.

Abstract

Integral quantum Hall plateau transitions in a planar lattice system due to gap collapse can be described by an effective field theory with Dirac fermions. We discuss how to reproduce the correct integral values for the Hall conductance, $\sigma_{xy}$, before and after the plateau transition, which are dictated by the microscopic topological invariant. In addition to the massless Dirac fermions that appear at gap closing, the matching condition of $\sigma_{xy}$ requires the introduction of massive Dirac fermions, as "spectators", in the effective field theory. For non-interacting electrons on the lattice, we give a general prescription to determine these massive "spectators", based on microscopic information on the vortices in the magnetic Brillouin zone which are closely related to edge states. Our description is demonstrated in a model with both nearest-neighbor and next-nearest-neighbor hoppings.