Sweeping cluster algorithm for quantum spin systems with strong geometric restrictions

TL;DR

This paper introduces a new quantum Monte Carlo 'sweeping cluster' algorithm tailored for quantum spin systems with strict geometric constraints, enabling more accurate and larger-scale simulations of complex quantum phases.

Contribution

The paper presents an efficient, exact Monte Carlo algorithm that inherently respects geometric restrictions, improving simulation accuracy and scalability for quantum spin models.

Findings

Demonstrated high accuracy on quantum dimer models

Achieved larger system sizes than previous methods

Validated the algorithm's reliability and efficiency

Abstract

Quantum spin systems with strong geometric restrictions give rise to rich quantum phases such as valence bond solids and spin liquid states. However, the geometric restrictions often hamper the application of sophisticated numerical approaches. Based on the stochastic series expansion method, we develop an efficient and exact quantum Monte Carlo "sweeping cluster" algorithm which automatically satisfies the geometrical restrictions. Here we use the quantum dimer model as a benchmark to demonstrate the reliability and power of this algorithm. Comparing to existing numerical methods, we can obtain higher accuracy results for a wider parameter region and much more substantial system sizes.