Quantum Quasi-Monte Carlo Technique for Many-Body Perturbative Expansions

TL;DR

This paper introduces a quantum quasi-Monte Carlo method that significantly accelerates high-order perturbative calculations in quantum many-body systems, outperforming traditional Monte Carlo techniques with faster convergence and practical efficiency.

Contribution

The authors adapt low-discrepancy sequence integration methods to quantum many-body perturbation theory, achieving orders-of-magnitude speed-ups over existing diagrammatic Monte Carlo approaches.

Findings

Speed-ups of several orders of magnitude in computational time.

Scaling as fast as 1/N with sample size, faster than traditional Monte Carlo.

Successful application to the Kondo ridge problem in quantum dots.

Abstract

High order perturbation theory has seen an unexpected recent revival for controlled calculations of quantum many-body systems, even at strong coupling. We adapt integration methods using low-discrepancy sequences to this problem. They greatly outperform state-of-the-art diagrammatic Monte Carlo. In practical applications, we show speed-ups of several orders of magnitude with scaling as fast as $1/N$ in sample number $N$; parametrically faster than $1/\sqrt{N}$ in Monte Carlo. We illustrate our technique with a solution of the Kondo ridge in quantum dots, where it allows large parameter sweeps.