The scaling exponent $g$ of the quasiparticle propagator for incompressible fractional quantum Hall states in the Laughlin sequence is expected to be robust against perturbations that do not close the gap. Utilizing a novel AlGaAs/GaAs heterostructure designed to produce sharp edge confinement, we probe the robustness of the chiral Luttinger liquid at the boundary of the $\nu =1/3$ state by measuring the tunneling conductance between counterpropagating edge modes. We demonstrate that for transmission $t\ge 0.7$ the tunneling conductance is well-described by the first two terms of a perturbative series expansion corresponding to $g=1/3$. We demonstrate that the measured scaling exponent is robustly pinned to $g=1/3$ across the plateau, only deviating as the bulk state becomes compressible. We examine the impact of weak disorder on the scaling exponent, finding it insensitive. These measurements establish the topological robustness of anyon tunneling at $\nu =1/3$ and substantiate the chiral Luttinger liquid description of the edge mode.

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• Anyons
• Edge states
• Fractional quantum Hall effect
• Quantum transport
• Topological phases of matter
• Fabry-Pérot interferometry