Projective Truncation Approximation for Equations of Motion of Two-Time Green's Functions

TL;DR

This paper introduces a new operator projection method for truncating equations of motion in two-time Green's functions, ensuring physical properties and improving accuracy over traditional approaches, demonstrated on the Anderson impurity model.

Contribution

The paper proposes a practical operator projection truncation method that preserves causality, invariance, and symmetry in two-time Green's functions, improving upon conventional methods.

Findings

Guarantees causality and symmetry in Green's functions.

Shows improved results over traditional Lacroix approximation.

Analyzes Kondo screening distribution in energy space.

Abstract

In the equation of motion approach to the two-time Green's functions, conventional Tyablikov-type truncation of the chain of equations is rather arbitrary and apt to violate the analytical structure of Green's functions. Here, we propose a practical way to truncate the equations of motion using operator projection. The partial projection approximation is introduced to evaluate the Liouville matrix. It guarantees the causality of Green's functions, fulfills the time translation invariance and the particle-hole symmetry, and is easy to implement in a computer. To benchmark this method, we study the Anderson impurity model using the operator basis at the level of Lacroix approximation. Improvement over conventional Lacroix approximation is observed. The distribution of Kondo screening in the energy space is studied using this method.