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

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 ${\ensuremath{\chi}}_{q}^{R}(k,\ensuremath{\omega})$, we obtain leading corrections to both the heat flux carried by the edge plasmon and to its spectrum. Two generic regimes emerge: (i) a gapped, local dielectric response with finite-range coupling, producing a negative correction to the quantized heat flux that scales as ${T}^{4}$ at low temperatures together with a convex cubic shift of the plasmon dispersion, and (ii) a hydrodynamic (diffusive) response with relaxation, yielding a crossover from ${T}^{4}$ to ${T}^{3/2}$ scaling and a change of sign in the correction. We further introduce a microscopic dipolar model in which the edge couples electrostatically to localized dipole moments inside a wide compressible strip. This long-rang