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

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.

35 pages, 20 figures

References in corpus (24)

• One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
• Quantum Monte Carlo with Directed Loops
• Bosonizing one-dimensional cold atomic gases
• The one-dimensional Bose-Hubbard Model with nearest-neighbor interaction
• Worm algorithms for classical statistical models
• Dynamics and Thermodynamics of the Bose-Hubbard model
• Generalized event-chain Monte Carlo: Constructing rejection-free global-balance algorithms from infinitesimal steps
• Superfluid--Insulator Transition in Commensurate Disordered Bosonic Systems:Large-Scale Worm-Algorithm Simulations
• Superfluid-Superfluid Phase Transitions in Two-Component Bose System
• Cluster Monte Carlo Algorithm for the Quantum Rotor Model
• Sign-Alternating Interaction Mediated by Strongly-Correlated Lattice Bosons
• Event-chain Monte Carlo for classical continuous spin models
• Directed geometrical worm algorithm applied to the quantum rotor model
• Event-chain algorithm for the Heisenberg model: Evidence for $z\simeq 1$ dynamic scaling
• A cluster algorithm for resistively shunted Josephson junctions
• Nonperturbative functional renormalization-group approach to the sine-Gordon model and the Lukyanov-Zamolodchikov conjecture
• Correlations in the Sine-Gordon Model with Finite Soliton Density
• The Generic, Incommensurate Transition in the two-dimensional Boson Hubbard Model
• Scaling Exponents in the Incommensurate Phase of the Sine-Gordon and U(1) Thirring Models
• Majorana zero modes and their bosonization
• Thermal depinning and transverse-field tilting transitions in a planar vortex array pinned by a columnar defect
• Dissipative Effects on the Superfluid to Insulator Transition in Mixed-dimensional Optical Lattices
• One dimensional Bose-Hubbard model with long range hopping
• Bosonized one-dimensional quantum systems through enhanced event-chain Monte Carlo