Efficient treatment of the high-frequency tail of the self-energy function and its relevance for multi-orbital models

TL;DR

This paper introduces an efficient, noise-free method for accurately computing the high-frequency tail of the self-energy in quantum Monte Carlo simulations, enhancing the study of complex multi-orbital systems within dynamical mean-field theory.

Contribution

It presents a novel, cost-effective approach to improve the stability and accuracy of the self-energy calculation in CT-HYB simulations, applicable to multi-orbital models with complex interactions.

Findings

The method effectively captures the high-frequency behavior of the self-energy.

Application to a two-orbital Anderson impurity model reveals phase transitions.

The approach accelerates calculations for systems with complicated band structures.

Abstract

In this paper, we present an efficient and stable method to determine the one-particle Green's function in the hybridization-expansion continuous-time (CT-HYB) quantum Monte Carlo method, within the framework of the dynamical mean-field theory. The high-frequency tail of the impurity self-energy is replaced with a noise-free function determined by a dual-expansion around the atomic limit. This method does not depend on the explicit form of the interaction term. More advantageous, it does not introduce any additional numerical cost to the CT-HYB simulation. We discuss the symmetries of the two-particle vertex, which can be used to optimize the simulation of the four-point correlation functions in the CT-HYB. Here, we adopt it to accelerate the dual-expansion calculation, which turns out to be especially suitable for the study of material systems with complicated band structures. As an application, a two-orbital Anderson impurity model with a general on-site interaction form is studied. The phase diagram is extracted as a function of the Coulomb interactions for two different Hund's coupling strengths. In the presence of the hybridization between different orbitals, for smaller interaction strengths, this model shows a transition from metal to band-insulator. Increasing the interaction strengths, this transition is replaced by a crossover from Mott insulator to band-insulator behavior.