Non-linear edge dynamics of the Laughlin state

In this presentation, we will explore the non-linear edge dynamics of the Laughlin states. These dynamics are derived from the Chern-Simons-Ginzburg-Landau theory with appropriate boundary conditions, which are compatible with the gauge-anomaly dynamics at the edge of the sample. By employing a systematic perturbation scheme based on scaling analysis, we have assigned dispersive and non-linear terms in the fluid dynamic equations of the Laughlin state at the same perturbation order. As a result, we have derived the Korteweg-de-Vries equation as the weakly non-linear dynamics of the edge states, along with the boundary Hamiltonian of the system. Hence, this work extends the conventional Chiral Luttinger Liquid theory for the edge of the Fractional Quantum Hall (FQH) system by incorporating systematic higher-gradient and non-linear corrections.

In conclusion, we will discuss how quantizing this edge KdV dynamics can provide a more comprehensive way to study non-linear quantum transport at the edge of the FQH state, since this approach goes beyond the traditional topological quantum field theory framework associated with the FQH state.