Persistence of basis compression for two-particle Green’s functions

Determine whether the favorable basis compression observed for the one-particle impurity spectral function persists when sample-based Krylov subspaces are used to evaluate two-particle Green’s functions and the associated local vertex functions.

Background

The paper proposes extending the sample-based Krylov framework beyond single-particle Green’s functions to two-particle Green’s functions and local vertex functions. Such quantities are required by diagrammatic extensions of dynamical mean-field theory, including parquet, dynamical vertex, and dual-fermion approaches.

The proposed extension would use Krylov subspaces generated from two-particle seed states. However, the paper does not establish whether the strong reduction in basis size found for the one-particle spectral function survives at the two-particle level, where the relevant excitation structure and computational demands are more complex.