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The orthogonality catastrophe in a Tomonaga-Luttinger liquid with an impurityis reexamined for the case when the interaction parameter or the dimensionlessconductance is g=1/2. By transforming bosons back to fermions, the Hamiltonianis reduced to a quadratic form, which allows for explicit calculation of theoverlap integral and the local density of states at the defect site. Theexponent of the orthogonality catastrophe due to a backward scattering centeris found to be 1/8, in agreement with previous studies using differentapproaches. The time-dependence of the core-hole Green's function is computednumerically, which shows a clear crossover from a non-universal short-timebehavior to a universal long-time behavior. The local density of statesvanishes linearly in the low-energy limit at g=1/2.Comment: 9 pages including 1 postscript figure, REVTeX, uses epsf.sty and  multicol.st

physical review. b, condensed matter

Local perturbation in a Tomonaga-Luttinger liquid at<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>g</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn><mml:mo>:</mml:mo></mml:math>Orthogonality catastrophe, Fermi-edge singularity, and local density of states

Local perturbation in a Tomonaga-Luttinger liquid atg=1/2:Orthogonality catastrophe, Fermi-edge singularity, and local density of states