Effect of Electron Correlation on the Integer Quantum Hall Effect

TL;DR

The work addresses how electron-electron correlations influence the integer quantum Hall effect (IQHE) on a two-dimensional square lattice under a strong perpendicular magnetic field. It employs a Hubbard model with Gutzwiller renormalization to capture correlation effects, producing a mixed-space Hamiltonian with renormalization parameters $\alpha_{j,s}$, $d_j$, and $\lambda_{j,s}$ that depend on position while respecting magnetic translation symmetry. The transverse conductivity is computed via the Kubo formula $\sigma_{xy}$, showing that increasing the onsite repulsion $U$ degrades the $ν=1$ quantization by closing the mobility gap between the $ν=1$ and $ν=2$ Landau levels through band bending caused by spatial modulations of $\alpha_{j,s}$ and $\lambda_{j,s}$. The results provide a correlation-driven mechanism for IQHE degradation that links to recent experiments and helps bridge integer and correlated (fractional) quantum Hall physics in real-space terms.

Abstract

We numerically investigate the effect of electron correlation on the integer quantum Hall effect in a square lattice. Increasing the correlation strength via the effective onsite repulsion parameter $U$ degrades the quantization of $ν= 1$ transverse conductance due to the interplay of correlation and the external magnetic field, which together induce periodic modulations in renormalized hopping parameters and site energies. Overall, this work demonstrates that the strength of electron correlation can significantly impact conductivity in the integer quantum Hall regime.

Figures (4)

• Figure 1: Schematic of the magnetized square lattice model illustrating nearest neighbor hopping parameterized by $t_a$ and $t_b$, lattice dimensions and perpendicular magnetic field $B$.
• Figure 2: Optimal parameters as a function of site index and $U$ ($q=20$); (top left) hopping renormalization $\alpha_{j,s}$, (top right) double occupancy $d_j$, (bottom left) site renormalization energies $\lambda_{j,s}$, and (bottom right) quasiparticle occupations $\bar{n}_{j,s}^{qp}$.
• Figure 3: Plots of transverse conductivity in units of $e^2/h$ vs. chemical potential $\mu$ (left) and corresponding $k_x$ ($k_y=0$) band dispersion (right) optimized for (a) $U=1t$ and (b) $U=5t$. The red line at top left is vertically offset by $+0.06$ for clarity.
• Figure S1: Plots of the band structures of (a) weakly correlated ($U=1t$) and (b) strongly correlated ($U=5t$) magnetized square lattice models. The bands on the left include the optimal site renormalization parameters $\lambda_{j,s}$ while those on the right do not.