Flow equation approach to the sine-Gordon model

A continuous sequence of infinitesimal unitary transformations is used to d iagonalize the quantum sine-Gordon model for beta (2) is an element of (2 p i, infinity). This approach can be understood as an extension of perturbati ve scaling theory since it links weak- to strong-coupling behavior in a sys tematic expansion: a small expansion parameter is identified and this param eter remains small throughout the entire flow unlike the diverging running coupling constant of perturbative scaling. Our approximation consists in ne glecting higher orders in this small parameter. We find very accurate resul ts for the single-particle/hole spectrum in the strong-coupling phase and c an describe the full crossover from weak to strong-coupling. The integrable structure of the sine-Gordon model is not used in our approach. Our new me thod should be of interest for the investigation of nonintegrable perturbat ions and for other strong-coupling problems. (C) 2001 Elsevier Science B.V. All rights reserved.