Inchworm quasi Monte Carlo for quantum impurities

TL;DR

This paper introduces a quasi Monte Carlo approach using Sobol sequences to improve the efficiency of inchworm Monte Carlo methods for quantum impurity models, enabling better handling of complex multi-orbital systems.

Contribution

It demonstrates the application of quasi Monte Carlo techniques to inchworm Monte Carlo, achieving enhanced convergence and extending applicability to more complex impurity models.

Findings

Achieved $1/N$ convergence with quasi Monte Carlo.

Extended inchworm method to multi-orbital Anderson impurity models.

Reduced computational cost for complex quantum impurity simulations.

Abstract

The inchworm expansion is a promising approach to solving strongly correlated quantum impurity models due to its reduction of the sign problem in real and imaginary time. However, inchworm Monte Carlo is computationally expensive, converging as $1/\sqrt{N}$ where $N$ is the number of samples. We show that the imaginary time integration is amenable to quasi Monte Carlo, with enhanced $1/N$ convergence, by mapping the Sobol low-discrepancy sequence from the hypercube to the simplex with the so-called Root transform. This extends the applicability of the inchworm method to, e.g., multi-orbital Anderson impurity models with off-diagonal hybridization, relevant for materials simulation, where continuous time hybridization expansion Monte Carlo has a severe sign problem.