Continuous-time auxiliary field Monte Carlo for quantum impurity models

Introduction. – The development of efficient numerical methods for solving quantum impurity models has been driven in recent years by the success of dynamical mean field theory (DMFT) [1–3] and its extensions. DMFT is an approximate framework for the study of fermionic lattice models, which replaces the lattice by a quantum impurity embedded in a self-consistent bath. Both cluster-extensions of DMFT [3–7] and realistic electronic structure calculations, which combine DMFT with band structure methods [3], involve multi-site or multiorbital impurity models (e.g. for dand f -electron systems), whose solution is computationally expensive and in practice the bottleneck of the calculations. In order to facilitate progress in this field, it is therefore important to develop fast and accurate impurity solvers.