Symmetry breaking and restoration using the equation-of-motion technique for nonequilibrium quantum impurity models

The dynamics of correlated electrons in quantum impurity models is typically described within the nonequilibrium Green function formalism combined with a suitable approximation. One common approach is based on the equation-of-motion technique often used to describe different regimes of the dynamic response. Here, we show that this approach may violate certain symmetry relations that must be fulfilled by the definition of the Green functions. These broken symmetries can lead to unphysical behaviour. To circumvent this pathological shortcoming of the equation-of-motion approach we provide a scheme to restore basic symmetry relations. Illustrations are given for the Anderson and double Anderson impurity models.