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

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.