Optical properties of quantum wires: Fermi-edge singularity exponents and the low-density limit

A simple many-body treatment of the Fermi-edge singularities in absorption and photoemission in quasi-one-dimensional quantum wires is presented. The problem of calculating the transition probabilities is reduced to numerically evaluating a sufficient number of determinants describing the overlap of the appropriate many-body wave functions. It is found that the edge singularity exponents can be determined from the size dependence of these determinants. The well-known connection between these exponents and the phase shifts at the Fermi surface are explicitly checked for one-dimensional quantum wires. The singular edge behavior is interpreted in terms of Friedel’s replacement transitions and is found to be due to a replacement transition to the bound state, a result confirmed by considering the evolution of the spectra in the low-density limit. © 1996 The American Physical Society.