Quantum Phase Transition between Integer Quantum Hall States of Bosons

TL;DR

This paper investigates quantum phase transitions between trivial insulators and bosonic Integer Quantum Hall phases, revealing conditions for direct transitions and describing the critical theory as massless QED-3 with fermionic vortices.

Contribution

It introduces a fermionic parton approach to describe the transition, identifying the critical point as massless QED-3 with Nf=2 fermion flavors, and explores conditions for direct transitions versus intervening superfluid phases.

Findings

Intervening superfluid phase generally appears between phases.

Additional symmetries can enable a direct transition.

Universal conductivity at the transition matches Dirac fermion resistivity.

Abstract

Bosonic Integer Quantum Hall (IQH) phases are a class of symmetry protected topological (SPT) phases that, similar to the fermionic IQH states, support a quantized Hall conductance. They, however, require interactions for their realization. Here we study quantum Hall plateau transitions between a trivial insulator and a bosonic IQH phase, in a clean system. Generically, we find an intervening superfluid phase. The presence of additional symmetries, however, can potentially lead to a direct transition between these phases. We employ a fermionic parton description that captures both the insulating phases as well as the transition between them. The critical theory is massless QED-3 with Nf = 2 fermion flavors. The fermions have a surprisingly simple interpretation - they are vortices of the superfluid. Therefore the universal conductivity at the transition, assuming it is continuous, equals the universal resistivity of Dirac fermions in QED-3. We also briefly comment on sigma model descriptions of the transition and the surface states of related 3D SPT phases.