Flow equation approach to the sine-Gordon model

Details Flow equation approach to the sine-Gordon model Flow equation approach to the sine-Gordon model

2000-06-26

arxiv.org/abs/cond-mat/0006403v1

Nucl.Phys. B592 (2001) 512-562

Physics

Condensed Matter

Statistical Mechanics

38 pages, 7 figures

Scientific paper

10.1016/S0550-3213(00)00507-1

A continuous sequence of infinitesimal unitary transformations is used to diagonalize the quantum sine-Gordon model for \beta^2\in(2\pi,\infty). This approach can be understood as an extension of perturbative scaling theory since it links weak- to strong-coupling behavior in a systematic expansion: a small expansion parameter is identified and this parameter remains small throughout the entire flow unlike the diverging running coupling constant of perturbative scaling. Our approximation consists in neglecting higher orders in this small parameter. We find very accurate results for the single-particle/hole spectrum in the strong-coupling phase and can 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 method should be of interest for the investigation of nonintegrable perturbations and for other strong-coupling problems.

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