# Controllable Precision of the Projective Truncation Approximation for Green's Functions

## TL;DR

This paper demonstrates that the projective truncation approximation for Green's functions offers controllable and systematically improvable accuracy in quantum many-body calculations, validated through the Anderson impurity model.

## Contribution

It introduces a quantitative gauge for truncation error and confirms the controllable precision of the method with larger operator bases.

## Key findings

- Results converge to NRG as basis size increases
- Proposed a quantitative gauge for truncation error
- Confirmed controllable precision of the approximation

## Abstract

Recently, we developed the projective truncation approximation for the equation of motion of two-time Green's functions (P. Fan et al., Phys. Rev. B 97, 165140 (2018)). In that approximation, the precision of results depends on the selection of operator basis. Here, for three successively larger operator bases, we calculate the local static averages and the impurity density of states of the single-band Anderson impurity model. The results converge systematically towards those of numerical renormalization group as the basis size is enlarged. We also propose a quantitative gauge of the truncation error within this method and demonstrate its usefulness using the Hubbard-I basis. We thus confirm that the projective truncation approximation is a method of controllable precision for quantum many-body systems.