Abstract
The phase diagram for interacting electrons can be determined from the one-loop renormalization group (RG) analysis in weak coupling. However, the lack of analytic solutions for the RG flow equations often makes identifying the relevant and irrelevant couplings vague. Here we propose a scaling Ansatz to classify the relevant couplings without ambiguity. This powerful classification scheme allows us to clarify a controversial quantum phase transition in the doped two-leg ladder. With the help of the scaling Ansatz, the mistaken quantum phase transition turns out to be a non-trivial crossover with an interesting hierarchy of excitation gaps. The classification scheme we developed is rather general and can be applied to other renormalization group methods as well. © 2009 Elsevier B.V. All rights reserved.