Jeudi 27 juin 2013 à 10h15
Salle 234, Ecole de Physique

Duality of weak and strong scatterer in Luttinger liquid coupled to phonons

Oleg Yevtushenko, LMU, Munich, Germany

We study a Luttinger liquid with an embedded impurity, which is either a weak scatterer (WS) or a weak link (WL), when interacting electrons are additionally coupled to 1d massless bosons (e.g., acoustic phonons) [1]. We find that the duality relation, $Delta_{ws}Delta_{wl}=1 $, between scaling dimensions of the electron backscattering in the WS and WL limits, established for the standard LL, holds true in the presence of this additional coupling. Surprisingly, the duality exists for an arbitrary fixed strength of boson scattering from the impurity. This means that, at low temperatures, the system always remains either an ideal insulator or an ideal conductor, unless fermion and boson scattering from the impurity are correlated. We briefly review the new method, which allows one to reveal the duality relations for the case when all subsystems are either ideal conductors or insulators, and its generalization for the arbitrary phonon scattering [2]. [1] I. V. Yurkevich, A. Galda, O. M. Yevtushenko, I. V. Lerner, Phys. Rev. Lett. 110, 136405 (2013) [2] I. V. Yurkevich, submitted to PRL; I. V. Yurkevich, O. M. Yevtushenko, in progress.