Fermi-edge singularity in one-dimensional systems

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Abstract
The Fermi-edge singularity in optical spectra is studied theoretically using the Tomonaga-Luttinger model for one-dimensional (1D) systems. Its critical exponent is obtained analytically for an arbitrary mass of a valence hole taking into account the electronic correlation. The exponent is found to be independent of the hole dynamics in 1D, which is in striking contrast to the 2D and 3D cases. Weak repulsive interaction among the conduction electrons sharpens the power-law peak in the edge spectrum.