Year: 2007
Type: article
Abstract: We investigate the indirect interaction between two isolated impurities in a Luttinger liquid described by a microscopic lattice model. To treat the electron-electron interaction $U$, the functional renormalization group method is used. For comparison, we also study the $U=0$ case. We find that for a wide range of impurity parameters the impurity interaction ${V}_{12}$ as a function of their separation $r$ oscillates with decaying amplitude between being attractive and repulsive. For half-filling of the band and in a crossover regime between weak and strong impurities, the interaction becomes purely attractive. For $U=0$ and independent of the impurity strength, the amplitude of the interaction energy falls off as $1∕r$. For $U>0$, the decay for small separations and weak to intermediate impurities is governed by a $U$ dependent exponent larger than $\ensuremath{-}1$, which crosses over to $\ensuremath{-}1$ for large $r$. The crossover scale depends on the impurity strength and $U$. We present simple pictures which explain our results in the limits of weak and strong impurities. We finally also consider attractive interactions $U<0$.
Source: Physical Review B
Authors: P. Wächter, V. Meden, K. Schönhammer
Institution: University of Göttingen
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1976343560