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

TL;DR

This paper introduces a novel method using continuous unitary transformations and operator product expansion to analyze the sine-Gordon model across weak to strong coupling regimes, providing accurate gap predictions.

Contribution

It develops a systematic extension of perturbative scaling theory to connect weak and strong-coupling behaviors in the sine-Gordon model.

Findings

Accurately predicts the single-particle gap in the strong-coupling phase.

Provides a systematic approach applicable to other vertex operator-based strong-coupling problems.

Demonstrates the effectiveness of continuous unitary transformations in quantum field models.

Abstract

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 2 pi < beta^2 < 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 approach should also be useful for other strong-coupling problems that can be formulated in terms of vertex operators.