For two decades, the Hirsch-Fye algorithm, which uses a discrete Hubbard-Stratonovich transformation to decouple interaction terms, and exact diagonalization have been the methods of choice. Hirsch-Fye type methods require a fine grid spacing to capture the short time behavior of the Green function, which makes simulations at low temperature and strong interactions prohibitive, while exact diagonalization represents the continuous density of states of the reservoir by a small number of levels.

Recently, a new class of impurity solvers has been developed, based on the stochastic evaluation of a diagrammatic expansion of the partition function and the resummation of diagrams into determinants. Two complimentary approaches are possible: a weak-coupling expansion in powers of the coupling constants or a strong-coupling expansion in powers of the impurity-bath mixing. These algorithms require neither auxiliary fields nor a time discretization.

I will discuss the strong coupling approach in a representation which is suitable for density-density interactions (the general formulation for models with exchange and pair hopping terms will be presented during the conference). The important feature is that the perturbation order which is needed decreases as the interaction strength is increased. I will demonstrate that the new algorithm allows unprecedented access to the low-temperature physics for interaction strengths of the order of the Mott critical value.