Sum rule violation in self-consistent hybridization expansions

TL;DR

This paper investigates sum rule violations in self-consistent hybridization expansions for multi-orbital quantum impurity models, showing that certain approximations violate fundamental sum rules, with implications for their reliability.

Contribution

It identifies and analyzes sum rule violations in non-crossing and one-crossing approximations, highlighting the superiority of the one-crossing method.

Findings

Sum rule violations are more severe with multiple orbitals and away from particle-hole symmetry.

The one-crossing approximation outperforms the non-crossing approximation.

Sum rule adherence correlates with the reliability of the approximations.

Abstract

We show that for multi-orbital quantum impurity models the non-crossing approximation and one-crossing approximation versions of the self-consistent hybridization expansions violate the sum rules relating the coefficients of the high-frequency expansion of the self energy and the product of the self energy and Green function to thermodynamic expectation values. Comparison of non-crossing/one-crossing results to numerically exact quantum Monte-Carlo calculations shows that the consistency with sum rules provides a useful estimate of the reliability of the approximations. The sum rule violations are more pronounced, and therefore the quality of the non-crossing/one-crossing approximation is poorer, in situations with multiple orbitals and away from particle-hole symmetry but becomes less severe as the correlation strength increases. The one crossing approximation is markedly superior to the non-crossing approximation.