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arXiv:hep-lat/9408005 · Physica A Statistical Mechanics and its Applications

The sine Gordon model: perturbation theory and cluster Monte Carlo

Martin Hasenbusch B, M Marcu, K. Pinn

Published Nov 1, 1994• 12 citations
arXivHTMLPDF
DOI
10.1016/0378-4371(94)00196-0

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The authors study here the sine-Gordon quantum field theory, relevant for many 1D gapped systems and experimental settings. Despite its integrability, computing correlation functions, especially at finite temperatures, remains challenging. Existing methods like perturbative expansions, Monte Carlo simulations, and Hamiltonian truncation have limitations. The authors develop here a numerical approach using the method of random surfaces, which is efficient, scalable, and free from the sign problem. They validate their results against established techniques and propose future applications for multipoint functions and quench dynamics.
The generic Mott transition in one-dimensional quantum systems can be described by the sine-Gordon model with a tilt via bosonization. Because the configuration space of the sine-Gordon model separates into distinct topological sectors, standard local Monte Carlo schemes are limited to very small system sizes. To overcome this limitation, we introduce the smooth worm (SmoWo) Monte Carlo algorithm which enlarges the configuration space to allow smooth transitions between topological sectors. The method combines worm updates with event-chain Monte Carlo moves. We explicitly prove its validity and quantify its performance. Thanks to the substantial acceleration achieved by the SmoWo algorithm, we are able to simulate large system sizes, providing a precise picture of the different phases and critical behaviour of the sine-Gordon model.