Quantum impurity solvers using a slave rotor representation

TL;DR

This paper introduces a novel slave rotor representation for electron operators, leading to a new impurity solver method that smoothly interpolates between atomic and weak-coupling limits, suitable for Dynamical Mean-Field Theory applications.

Contribution

A new slave rotor-based method for solving multi-orbital Anderson impurity models at finite U, avoiding causality violations and enabling efficient studies at large orbital degeneracies.

Findings

Accurate description of the Mott transition.

Smooth interpolation between atomic and weak-coupling regimes.

Efficient for large orbital degeneracies.

Abstract

We introduce a representation of electron operators as a product of a spin-carry ing fermion and of a phase variable dual to the total charge (slave quantum rotor). Based on this representation, a new method is proposed for solving multi-orbital 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 non-crossing approximation, the new 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.