Optimization and implementation of novel quantum Monte Carlo methods for strongly correlated electron systems


Prof. Dr. Fakher Assaad
Institut fur Theoretische Physik
Universität Würzburg

Project Summary

The quantum mechanical many body problem defines research in the solid state, nuclear and particle physics. There is an ever growing class of such problems that can be solved exactly on classical computers in polynomial time. This gives us the opportunity to unravel many aspects of emergent collective phenomena defined by the notion that the whole is more than the sum of its parts. To harness this progress we have implemented a general formulation of the so called auxiliary field quantum Monte Carlo method. Our open source package named Algorithms for Lattice Fermions, is accessible at http://alf.physik.uni-wuerzburg.de and the documentation has been published in Ref. [1]. The implementation is efficiently parallelized using OpenMP/MPI and performs well on high-performance computers, as tested on JURECA and SuperMUC. It provides standards for the definition of very general models, lattice structure, and observables. QMC being a stochastic approach, ALF also includes an error analysis library. The motivation for such a project is to secure our know-how in a structured, robust and well documented program package. This allows new generations of doctoral students and postdoctoral researchers to profit from past
algorithmic development and optimization and efficiently investigate new problems. It also allows us to reproduce published results and to play with new ideas at minimal programming costs. Development of ALF will continue in the future.



Selected Publications

[1] M. Bercx, F. Goth, J. S. Hofmann, F. F. Assaad The ALF (Algorithms for Lattice Fermions) project release 1.0. Documentation for the auxiliary field quantum Monte Carlo code, arXiv:1704.00131, SciPost Phys. 3 (2017), 013.

[2] M. Bercx, J. S. Hofmann, F. F. Assaad, T. C. Lang, Spontaneous particle-hole symmetry breaking of correlated fermions on the Lieb lattice, Phys. Rev. B 95, 035108 (2017).

[3] ALF project public Git repository: https://alf.physik.uni-wuerzburg.de