Sum rule violation in self-consistent hybridization expansions.

We show that for multiorbital quantum impurity models the noncrossing 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's function to thermodynamic expectation values. Comparison of noncrossing/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 noncrossing/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 noncrossing approximation. [ABSTRACT FROM AUTHOR]