Composite-Fermion Study of Cavity-Modified Fractional Quantum Hall Excitation Gaps

We investigate how cavity-mediated attractive electron-electron interactions modify the excitation gaps of fractional quantum Hall states within the composite-fermion framework. We compute both the neutral magnetoroton excitation spectrum and the charged excitation gap relevant to transport experiments for the Laughlin $\nu=1/3$ and $\nu=1/5$ states. We consider a spin-polarized lowest-Landau-level model in which the interaction is mediated by a cavity mode with a spatially uniform vacuum-field gradient and a finite interaction range controlled by a long-distance cutoff. Finite-size scaling reveals that the transport gap is consistently enhanced by the cavity-induced interaction, with the gap enhancement scaling quadratically with the electron number and with the fourth power of the vacuum-field gradient. By contrast, the magnetoroton spectrum exhibits a richer dependence on the interaction range. The high-$k$ magnetoroton gap is enhanced for all interaction ranges considered, consistent with its close connection to the charged excitation gap, even with the long-range character of the interaction.