Comment on chern-Simons theory and atypical Hall conductivity in the Varma phase
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In a recent paper [Phys. Rev. B 97, 075135 (2018)PRBHB72469-995010.1103/PhysRevB.97.075135], Menezes et al. analyze the topological behavior of an effective bosonic model defined on the Lieb lattice in the 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 jeopardize the main result in this system.