In this Letter, we investigate the dissipative dynamics at the edge of Laughlin fractional quantum Hall (FQH) states starting from the hydrodynamic framework of the composite boson theory recently developed by G. M. Monteiro et al. [Phys. Rev. B 109, 174525 (2024)]. Critical to this description is the choice of boundary conditions, which ultimately stems from the choice of hydrodynamic variables in condensate degrees of freedom. Given the gapped nature of bulk, one would expect dissipation effects to play an important role only near the FQH edge. Thus, one envisions a scenario where the bulk hydrodynamic equations remain unmodified, while the dissipation effects are introduced at the edge via boundary conditions. We have recently shown that the anomaly requirements fix the boundary conditions of the FQH fluid to be no-penetration and no-stress boundary conditions. In this work, we introduce energy dissipation in the no-stress boundary condition leading to charge diffusion at the boundary. The resulting dissipative edge dynamics is quite rigid from a hydrodynamic perspective, as it has to preserve the edge charge continuity and the anomaly structure. We show that the diffusive edge dynamics with fluctuation-dissipation relations within a power counting scheme belong to the Kardar-Parisi-Zhang universality class.

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• Fractional quantum Hall effect
• Strongly correlated systems
• Kardar–Parisi–Zhang equation