Flow equation solution for the weak- to strong-coupling crossover in the sine-Gordon model

A continuous sequence of infinitesimal unitary transformations, combined with an operator product expansion for vertex operators, is used to diagonalize the quantum sine-Gordon model for beta(2) epsilon (2 pi, infinity). The leading order of this approximation already gives very accurate results for the single-particle gap in the strong-coupling phase. This approach can be understood as an extension of perturbative scaling theory since it links weak- to strong-coupling behavior in a systematic expansion. The method should also be useful for other strong-coupling problems that can be formulated in terms of vertex operators.