Quantum impurity solvers using a slave rotor representation

We introduce a representation of electron operators as a product of a spin-carrying fermion and of a phase variable dual to the total charge (slave quantum rotor). Based on this representation, a method is proposed for solving multiorbital Anderson quantum impurity models at finite interaction strength U. It consists in a set of coupled integral equations for the auxiliary field Green’s functions, which can be derived from a controlled saddle point in the limit of a large number of field components. In contrast to some finite-$U$ extensions of the noncrossing approximation, the method provides a smooth interpolation between the atomic limit and the weak-coupling limit, and does not display violation of causality at low frequency. We demonstrate that this impurity solver can be applied in the context of dynamical mean-field theory, at or close to half-filling. Good agreement with established results on the Mott transition is found, and large values of the orbital degeneracy can be investigated at low computational cost.