The generic Mott transition in the sine-Gordon model through an embedded worm algorithm

TL;DR

This paper introduces the SmoWo Monte Carlo algorithm, enabling large-scale simulations of the sine-Gordon model to better understand the Mott transition in one-dimensional quantum systems.

Contribution

The paper presents a novel smooth worm Monte Carlo algorithm that efficiently explores topological sectors in the sine-Gordon model, overcoming previous size limitations.

Findings

Efficient simulation of large system sizes.

Detailed characterization of phases and critical behavior.

Validation of the SmoWo algorithm's accuracy and performance.

Abstract

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.