Refermionized theory of the edge modes of a fractional quantum Hall cloud

Abstract: Making use of refermionization techniques, we map the nonlinear chiral Luttinger liquid model of the edge modes of a spatially confined fractional quantum Hall cloud developed in our recent work [Phys. Rev. A {\bf 107}, 033320 (2023)] onto a one-dimensional system of massive and interacting chiral fermions, whose mass and interactions are set by the filling factor of the quantum Hall fluid and the shape of the external anharmonic confining potential at the position of the edge. As an example of the predictive power of the refermionized theory, we report a detailed study of the dynamic structure factor and of the spectral function of a fractional quantum Hall cloud. Among other features, our refermionized theory provides a physical understanding of the effective decay of the edge excitations and of the universal power-law exponents at the thresholds of the dynamic structure factor. The quantitative accuracy of the refermionized theory is validated against full two-dimensional calculation based on a combination of exact diagonalization and Monte-Carlo sampling.