Exact Diagonalization at the Petaflop Scale

Exact diagonalization (ED) is an unbiased and versatile method to study a large variety of quantum many-body systems, ranging from quantum chemistry and nuclear structure calculations to correlated systems in condensed matter physics and ultracold atomic gases. In the first funding period of this project within the research unit 1807 we have successfully developed a flexible message-passing interface (MPI) based parallel exact diagonalization code for quantum spin models. We have applied this and related codes to several current problems in frustrated quantum magnetism and correlated fermions, and started an activity on energy spectroscopy of quantum critical points in 2+1 space- time dimensions. The purpose of this project in the next funding period is to further develop and apply a state-of-the-art ED framework for quantum spin and fermionic lattice models, and in a second step also for simple quantum field theories.

Quantum mechanical effects as well as strong interactions between the electrons play a prominent role in solid state materials at lowest temperatures. These two ingredients can lead to fascinating new physical effects, yet the equations describing these systems pose major problems for theoretical physicists. Massive computer simulations on supercomputers are often necessary to gain insight into the behavior of these systems. The goal of our project has been to predict novel states of matter in these materials and to develop simulation software therefore. These discoveries were made possible by a technical breakthrough in the simulation software we developed. The computational effort for this kind of computations grows exponentially with the number of simulated particles, i.e. for every additional particle we have to use twice the computational resources. Since we are interested in the collective behavior of many particles it is important to simulate as much particles as possible. Our software is now for the first time worldwide able to simulate 50 Spin 1/2 particles. It thus gives us a powerful tool to discover further interesting physical phenomena.