2007/03/05 by P. Wächter, P. Waechter, V. Meden +2
Physics and Astronomy · #Amplitude #Cold Atom Physics and Bose-Einstein Condensates #Condensed matter physics #Crossover #Electron #Exponent #Impurity #Lattice (music) #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum and electron transport phenomena #Quantum mechanics #Renormalization #Scaling #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.76.045123
published as Phys. Rev. B 76, 045123 (2007) · 8 pages, 9 figures included
arxiv created 2007/03/05 · openalex publication_date 2007/07/31 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 V12 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.