The generic Mott transition in one-dimensional quantum systems can be described by the $(1+1)D$ 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 ($\sim 15\times 15$). 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 up to $256\times 256$, providing a precise picture of the different phases and critical behavior of the sine-Gordon model.

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• Mott-superfluid transition
• Sine-Gordon equation
• Bosonization
• Monte Carlo methods