# Continuous-time quantum Monte Carlo calculation of multi-orbital vertex asymptotics

## TL;DR

This paper develops a method to accurately compute the high-frequency behavior of two-particle vertex functions in multi-orbital impurity models using continuous-time quantum Monte Carlo, improving the precision of non-local susceptibility calculations.

## Contribution

It derives equations linking vertex asymptotics to equal-time Green's functions and demonstrates their application in DMFT for multi-orbital systems, reducing uncertainties.

## Key findings

- High-frequency asymptotics can be efficiently computed from Green's functions.
- Knowledge of asymptotics reduces statistical errors in vertex calculations.
- Method improves non-local susceptibility calculations in DMFT extensions.

## Abstract

We derive the equations for calculating the high-frequency asymptotics of the local two-particle vertex function for a multi-orbital impurity model. These relate the asymptotics for a general local interaction to equal-time two-particle Green's functions, which we sample using continuous-time quantum Monte Carlo simulations with a worm algorithm. As specific examples we study the single-orbital Hubbard model and the three $t_{2g}$ orbitals of SrVO$_3$ within dynamical mean field theory (DMFT). We demonstrate how the knowledge of the high-frequency asymptotics reduces the statistical uncertainties of the vertex and further eliminates finite box size effects. The proposed method benefits the calculation of non-local susceptibilities in DMFT and diagrammatic extensions of DMFT.