Saint-Petersburg State University
In my talk, I first review a method devised recently for the analysis of the well-known problem of one impurity in the Luttinger liquid. It is known since the pioneering work by Kane and Fisher that the repulsion between the electrons leads to the enhancement of the scattering potential, so that even one impurity at low temperatures may effectively cut the quantum wire in two. We suggested a fermionic approach to this problem and a method of resummation of the most important diagrams, which reproduced the results known previously in the bosonization techniques. In the second part of my talk, I consider a Y-junction, connecting three interacting quantum wires within the same method. The Y-junction setup even in a simplified symmetric configuration is characterized by two conductances, whose evolution with interaction and temperature is governed by a set of coupled renormalization group (RG) equations. We find this set of RG equations non-perturbatively, by summing one-loop RG contributions in all orders of interaction. The fixed point structure and the implicit solution of these equations is presented. For sufficiently strong attractive interaction a new fixed point with unusual properties is found.