Strong coupling quantum impurity solver on the real and imaginary axis

TL;DR

This paper introduces a strong coupling diagrammatic Monte Carlo method for quantum impurity problems, demonstrating rapid convergence and high precision in spectral and transport calculations within DMFT.

Contribution

It develops a strong coupling expansion approach that is efficiently implementable on both real and imaginary axes, improving impurity solver accuracy and performance.

Findings

Rapid convergence with respect to expansion order

High-precision spectral and transport results

Benchmark comparisons with NRG calculations

Abstract

The diagramatic Monte Carlo method has so far been primarily used in connection with the weak coupling expansion. Here we show that the strong coupling expansion offers a significant advantage: it can be efficiently implemented on both the real and the imaginary axis at finite temperature. Using the example of a quantum impurity solver for the Dynamical Mean Field Theory (DMFT) problem, we illustrate rapid convergence with respect to the expansion order. We derive a closed-form expression for the Feynman diagrams of arbitrary order on the real axis. Employing these Feynman rules, we implement the bold hybridization-expansion quantum Monte Carlo (BHQMC) impurity solver and compare its performance to state-of-the-art results from Numerical Renormalization Group calculations of the Mott transition within DMFT applied to the Hubbard model. We demonstrate its power in providing a very precise frequency dependent scattering rate at finite temperature, enabling accurate spectroscopy calculations and delivering benchmark results for transport within DMFT.