Comment on "Chern-Simons theory and atypical Hall conductivity in the Varma phase''

TL;DR

This paper critiques a recent study claiming an atypical quantum Hall effect in a bosonic Lieb lattice model, highlighting inconsistencies that challenge the original findings.

Contribution

It provides a critical analysis of the previous work, identifying issues in the treatment of the propagator that question the validity of the claimed topological phenomena.

Findings

Identifies inconsistencies in the original propagator treatment

Questions the validity of the claimed quantum Hall effect

Highlights the need for careful theoretical analysis in topological models

Abstract

In a recent paper published in this Journal [Phys. Rev. B 97, 075135 (2018)], Menezes et al. analyze the topological behavior of a effective bosonic model defined on the Lieb lattice in presence of an electromagnetic field. In this context, the authors claim to have found an atypical quantum Hall effect for the quasiparticles. However, some inconsistencies related to the treatment of the propagator jeopardizes the main result in this system.