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Bulletin of the American Physical Society

Renormalization of a single impurity potential of arbitrary strength in a Tomonaga-Luttinger liquid

Kenji Kamide, Yuji Tsukada, Susumu Kurihara

Published Mar 15, 2006• 1 citation
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•Aug 18, 2016•2 citations
We study scaling of a single impurity potential in a Tomonaga‐Luttinger (TL) liquid for arbitrary impurity strength. Boson representation for the electron field operator including a phase shift by the impurity scattering is introduced, and used to calculate the temperature dependence of the local spectral density. The fixed line of an impurity potential is determined for TL liquid with spin dependent interactions (KS≠1), extending the results for weak and strong impurity limits to intermediate strength.
Transport through a spinless Tomonaga-Luttinger (TL) liquid is studied in the presence of a single impurity. A boundary bosonization technique is developed to treat an impurity of arbitrary strength. Our new bosonization formula (i) smoothly connects the ones for the strong and the weak impurity limits, and (ii) reproduces exact scaling equation for the transmission probability in the weak two-body interaction limit. With the use of our formula, TL parameter is determined from the long-distance correlation functions. The result indicates a possible renormalization of TL parameter due to the effect of the single impurity scattering.