Efficiency of quantum Monte Carlo impurity solvers for dynamical mean-field theory

TL;DR

This paper compares the efficiency of traditional Hirsch-Fye quantum Monte Carlo and newer continuous-time algorithms for solving impurity problems in dynamical mean-field theory, showing HF-QMC remains competitive when extrapolated properly.

Contribution

It provides a detailed quantitative comparison of Trotter errors in HF-QMC and demonstrates its competitiveness with CT-QMC when properly extrapolated.

Findings

HF-QMC with delta_tau extrapolation is competitive with CT-QMC.

Trotter errors in HF-QMC can be accurately estimated and controlled.

Proper extrapolation of delta_tau is crucial for reliable results.

Abstract

Since the inception of the dynamical mean-field theory, numerous numerical studies have relied on the Hirsch-Fye quantum Monte Carlo (HF-QMC) method for solving the associated impurity problem. Recently developed continuous-time algorithms (CT-QMC) avoid the Trotter discretization error and allow for faster configuration updates, which makes them candidates for replacing HF-QMC. We demonstrate, however, that a state-of-the-art implementation of HF-QMC (with extrapolation of discretization delta_tau -> 0) is competitive with CT-QMC. A quantitative analysis of Trotter errors in HF-QMC estimates and of appropriate delta_tau values is included.