Merging numerical renormalization group and intermediate representation to compactify two- and three-point correlators

TL;DR

This paper combines the numerical renormalization group with the intermediate representation to efficiently compress two- and three-point Green's functions on the real frequency axis, reducing memory usage in many-body calculations.

Contribution

It introduces a novel method that merges NRG and IR techniques to compactify complex Green's functions directly on the real frequency axis, improving computational efficiency.

Findings

IR can accurately reconstruct NRG data with low error

IR compression reduces memory requirements for Green's functions

The method is effective for two- and three-point correlators

Abstract

The vanguard of many-body theory is nowadays dealing with the full frequency dynamics of n-point Green's functions for n higher than two. Numerically, these objects easily become a memory bottleneck, even when working with discrete imaginary-time Matsubara frequencies. Here, we use the intermediate representation (IR) to compactify the two-point Green's function and three-point Fermion-Bose vertex directly on the real frequency axis, on the basis of numerical renormalization group (NRG) data. We empirically observe an upper bound of the relative error when comparing the IR reconstructed signal with the original NRG data, and demonstrate that a IR compacification is possible.