Field and Correlation-induced Closing of the Mobility Gap in the Square Lattice

Topological quantum systems have garnered widespread interest for their potential to advance technology ranging from quantum computing to topological catalysis. The integer quantum Hall effect (IQHE) is a paradigmatic manifestation of band topology which has led to innovations including metrological standards for electrical resistance and IQHE-based interferometers for probing anyonic quasiparticle statistics. Although its effects could be considered a perturbation, electron correlation is presumed to play a minor role in the IQHE. Here, we numerically investigate the effect of electronic correlations on the IQHE in a square lattice. We find that increasing the correlation strength via the effective onsite repulsion parameter U degrades the transverse conductance quantization of the first Landau level due to the interplay of correlation and the external magnetic field. Periodic modulations in renormalized hopping parameters and site energies ultimately explain the predicted conductivity degradation. Importantly, this work demonstrates how lattice models that go beyond a homogeneous treatment of Gutzwiller band renormalization can provide novel physical insight into the effect of correlation on the IQHE.