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.

• Received 1 August 2008

DOI:https://doi.org/10.1103/PhysRevLett.102.046806