# The Non-Crossing and One-Crossing solvers

The Non-Crossing approximation (Keiter and Kimball, PRL 25, 672 (1970)) and the one-crossing approximation (Pruschke, Z. Phys. B 74, 439 (1989)) are standard approximations to the hybridization expansion that work well in insulating (or almost insulating) systems. Here is a talk by Lei on the approximation

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Here are his slides and his detailed notes with derivations.

The Hybridiation expansion CT-QMC method in its single orbital and matrix version, as well as the boldNCA and boldOCA and the inchworm methods are closely related but numerically exact methods for sampling the hybridization expansion.