Improved Estimators for the Self-Energy and Vertex Function in Hybridization Expansion Continuous-Time Quantum Monte Carlo Simulations

TL;DR

This paper introduces efficient measurement techniques for the self-energy and vertex function in continuous-time quantum Monte Carlo simulations, significantly improving data accuracy and stability for analyzing strongly correlated electron systems.

Contribution

It presents a novel measurement method based on higher-order correlation functions and orthogonal polynomial filtering, enhancing the precision of self-energy and vertex function estimations.

Findings

Achieved unprecedented accuracy in Monte Carlo data.

Improved stability in analytical continuation processes.

Revealed significant vertex function changes in a two-orbital model.

Abstract

We propose efficient measurement procedures for the self-energy and vertex function of the Anderson impurity model within the hybridization expansion continuous-time quantum Monte Carlo algorithm. The method is based on the measurement of higher-order correlation functions related to the quantities being sought through the equation of motion, a technique previously introduced in the NRG context. For the case of interactions of density-density type, the additional correlators can be obtained at essentially no additional computational cost. In combination with a recently introduced method for filtering the Monte Carlo noise using a representation in terms of orthogonal polynomials, we obtain data with unprecedented accuracy. This leads to an enhanced stability in analytical continuations of the self-energy or in two-particle based theories such as the dual fermion approach. As an illustration of the method we reexamine the previously reported spin-freezing and high-spin to low-spin transitions in a two-orbital model with density-density interactions. In both cases, the vertex function undergoes significant changes, which suggests significant corrections to the dynamical mean-field solutions in dual fermion calculations.