Suppression of quantized heat flow by the dielectric response of a compressible strip at the quantum Hall edge

Abstract: We develop a unified perturbative framework for energy transport along a chiral quantum Hall (QH) edge coupled to a disordered, compressible strip. Treating the strip as a generic linear response environment characterized by its retarded susceptibility $\chi_q^R(k,\omega)$, we derive leading-order interaction corrections to both the edge heat flux and the plasmon spectrum. Two complementary regimes are analyzed: (i) a gapped, local dielectric response with finite-range coupling, which yields a universal negative $T^4$ correction to the quantized heat flux and a corresponding convex cubic term in the plasmon dispersion; and (ii) a hydrodynamic (diffusive) response with relaxation, producing a crossover from $T^4$ to $T^{3/2}$ scaling and a change of sign in the correction. The resulting backaction reduces the plasmon group velocity and can suppress the apparent thermal conductance by an amount consistent with experiment. Importantly, the total heat flux remains quantized: the apparent deficit in the plasmon contribution corresponds to an induced energy flow within the compressible strip, representing a form of heat drag between chiral and nonchiral modes. The framework thus provides a microscopic and quantitatively plausible explanation of the ``missing heat flux'' anomaly observed at QH edges and links its transport signature to the nonlinearity of the plasmon spectrum.