Effects of long- and short-range correlated interactions in an anisotropic flat-band fermion system
Phys. Rev. B 114, 055105 – Published 6 July, 2026
DOI: https://doi.org/10.1103/hdv8-f56n
Abstract
An anisotropic flat-band fermion system with linear dispersion along one direction and cubic dispersion along the other was proposed in Sheffer et al. [Phys. Rev. X 13, 021012 (2023)]. Here, we study the effects of long-range Coulomb interaction in this fermion system by renormalization group theory and the Dyson–Schwinger gap equation. Renormalization group analysis reveals that the fermion velocity is always restored along the direction that originally exhibits cubic dispersion. Consequently, in the low-energy regime, the system exhibits behavior similar to that of a two-dimensional Dirac fermion system subject to Coulomb interaction. Using the Dyson–Schwinger gap equation method, we find that an excitonic gap is generated if the Coulomb interaction is sufficiently strong, driving the system into a distinct excitonic insulating state with half-quantized anomalous Hall conductivity. Interestingly, we find that the excitonic gap is much more readily generated by Coulomb interaction in the anisotropic flat-band fermion system than in the Dirac fermion system. Based on this finding, we propose a strategy to observe the half-quantized anomalous Hall conductivity. We also investigate the influence of short-range four-fermion interaction on the anisotropic flat-band fermion system. It is shown that the system is driven into the excitonic insulating phase if the strength of four-fermion interaction exceeds a critical value. Observable quantities of this system in the free case, under weak Coulomb interaction, and in the gapped phase driven by strong interactions are also analyzed.
