Universal Dephasing in a Chiral 1D Interacting Fermion System

We consider dephasing by interactions in a one-dimensional chiral fermion system (e.g., a quantum Hall edge state). For finite-range interactions, we calculate the spatial decay of the Green's function at fixed energy, which sets the contrast in a Mach-Zehnder interferometer. Using a physically transparent semiclassical ansatz, we find a power-law decay of the coherence at high energies and zero temperature (T=0), with a universal asymptotic exponent of 1, independent of the interaction strength. We obtain the dephasing rate at T > 0 and the fluctuation spectrum acting on an electron