Mobile impurity in one-dimensional correlated electron systems

Critical properties of one-dimensional (1D) correlated electron systems with a mobile impurity are investigated. By applying the finite-size scaling method to a Bethe-ansatz solvable model, we derive the conformal dimensions related to the orthogonality catastrophe. We then apply the results to the Fermi-edge singularity in quantum wires, and clarify how the critical exponent for X-ray absorption depends on the mass of the core-hole created. A generalization to SU(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}\end{document}) electron systems is outlined based on the g-on description of 1D electron systems.