Weakly nonlinear dynamics of FQH edge: a hydrodynamic perspective

In this talk, I will discuss the weakly nonlinear dynamics of the Laughlin edge state. Starting from the Chern-Simons-Ginzburg-Landau (CSGL) theory in the lower half-plane, I will show that the edge density dynamics are governed by the Korteweg-de Vries (KdV) equation. The saddle point bulk dynamics of the CSGL action can be reformulated as two-dimensional compressible fluid dynamic equations, subject to a quantum Hall constraint that links superfluid vorticity to density fluctuations. The boundary conditions in this hydrodynamic framework include no-penetration and no-stress conditions, giving rise to an additional U(1) symmetry at the boundary. By employing the Hamiltonian framework for the KdV equation, I will show that the chiral Luttinger liquid theory is recovered in the linearized regime and provide a pathway for canonically quantizing the edge dynamics in the weakly nonlinear limit.