Multigrid Methods in Quantum Field Theory

Michael Lubasch, Pierre Moinier, Dieter Jaksch

Wayne Nicholas Polyzou, Tracie Michlin, Fatih Bulut

P.G. Lauwers

Conventional Monte Carlo simulation algorithms for models in statistical mechanics and quantum field theory are afflicted by problems caused by their locality. They become highly inefficient if investigations of critical or nearly-critical systems, i.e., systems with important large scale phenomena, are undertaken. We present two types of multiscale approaches that alleveate problems of this kind: stochastic cluster algorithms and multigrid Monte Carlo simulation algorithms. Another formidable computational problem in simulations of phenomenologically relevant field theories with fermions is the need for frequently inverting the Dirac operator. This inversion can be accelerated considerably by means of deterministic multigrid methods, very similar to the ones used for the numerical solution of differential equations. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nils Blümer

We present a new algorithm which allows for direct numerically exact solutions within dynamical mean-field theory (DMFT). It is based on the established Hirsch-Fye quantum Monte Carlo (HF-QMC) method. However, the DMFT impurity model is solved not at fixed imaginary-time discretization Delta_tau, but for a range of discretization grids; by extrapolation, unbiased Green functions are obtained in each DMFT iteration. In contrast to conventional HF-QMC, the multigrid algorithm converges to the exact DMFT fixed points. It extends the useful range of Delta_tau, is precise and reliable even in the immediate vicinity of phase transitions and is more efficient, also in comparison to continuous-time methods. Using this algorithm, we show that the spectral weight transfer at the Mott transition has been overestimated in a recent density matrix renormalization group study.

Santiago García

Santiago García, GERALD S. GURALNIK, John W. Lawson