Numerically exact quantum Monte Carlo algorithms for impurity problems

Within the last 20 years, the dynamical mean-field theory (DMFT) has been established as a standard approach for materials with strong electronic correlations. The DMFT reduces fermionic lattice problems to quantum impurity problems which have to be solved self-consistently. Thus, its predictive power depends on the availability of precise and efficient impurity solvers. Quantum Monte Carlo (QMC) based algorithms play a leading role in this respect. Their access to low temperatures T (which are of particular physical interest) is, however, limited by the scaling of the computational effort with T-3.

Recently, a new indirect impurity solver has been proposed, based on the determinantal quantum Monte Carlo (DQMC) method for which the effort grows only linearly with the inverse temperature. This advantage comes at the prize of systematic errors caused, primarily, by the Trotter discretization. The primary goal of this project is the elimination of these systematic errors, starting with the extension of the multigrid approach, developed by the project leader for the Hirsch-Fye QMC method, to the DQMC algorithm. In a second step, we will also try to find a direct continuous-time formulation of the determinantal method.