Computing quantum mechanics using HPC
Supercomputers in the USA, Europe, and Japan have proved indispensable for research into the effects of quantum mechanics at hugely different length scales. One investigation, just published in the journal Science, confirms the theory of the strong interaction in particle physics by exactly calculating the mass difference between the proton and the neutron. The other two investigations employed high-performance computing to look at the properties of superconductors, and to simulate from first-principles the dynamics of very large systems, potentially of millions of atoms.
Protons and neutrons are the main components of atomic nuclei and have almost but not quite the same mass: the neutron is about 0.14 per cent more massive than the proton. It is not entirely stable but can decay into a proton and a pion. The mass difference is key to the stability of atoms and thus the structure of matter as we know it, but it is paradoxical. Because the proton is electrically charged it should be the heavier particle, deriving a small extra contribution to its mass from the electromagnetic field.
Now, some 80 years after the discovery of the neutron, a team of physicists from France, Germany, and Hungary, headed by Zoltán Fodor, a researcher from Wuppertal, has finally calculated the tiny neutron-proton mass difference from first principles, using one of the most powerful computers in the world, Juqueen at the Forschungszentrum Jülich in Germany to perform the lattice quantum-chromodynamics and quantum-electrodynamics calculations.
The fact that the neutron’s mass is larger than the proton’s must be due to the different masses of their constituent quarks, and this is what Fodor and his team have now shown. For the calculations, the team developed a new class of simulation techniques combining quantum chromodynamics with quantum electrodynamics in order to determine the effects of electromagnetic interactions precisely.
According to professor Kurt Binder is chairman of the scientific council of the John von Neumann Institute for Computing: ‘Only using world-class computers, such as those available to the science community at Forschungszentrum Jülich, was it possible to achieve this milestone in computer simulation.’ Juqueen was supported in the process by its ‘colleagues’ operated by the French science organizations CNRS and GENCI as well as by the computing centres in Garching (LRZ) and Stuttgart (HLRS).
The results of this work by Fodor’s team of physicists from Bergische Universität Wuppertal, Centre de Physique Théorique de Marseille, Eötvös University Budapest, and Forschungszentrum Jülich open the door to a new generation of simulations of the properties of quarks, gluons, and nuclear particles. According to professor Kálmán Szabó of the Forschungszentrum Jülich: ‘In future, we will be able to test the standard model of elementary particle physics with a tenfold increase in precision, which could possibly enable us to identify effects that would help us to uncover new physics beyond the standard model.’ The paper describing their methods Ab initio calculation of the neutron-proton mass difference has just been published in Science.
A quantum-mechanical calculation at a very different length scale has been successfully carried out by David Bowler, from the International Center for Materials Nanoarchitectonics (MANA) in Japan and UCL London Centre for Nanotechnology, and Tsuyoshi Miyazaki at the National Institute for Materials Science. Using the Riken computer in Japan, they have successfully developed a highly efficient, large-scale, method for simulating from first-principles the dynamics of very large systems, potentially containing millions of atoms.
Until now, the size of the systems modelled with conventional first-principles methods has been limited to only a few hundred atoms (in most cases) because the complexity and time required for simulations increases as the cube of the number of atoms being modelled. The new method offers a way to perform atomic and electronic structure simulations of biological molecules and complex matter, including nanostructured materials.
They developed a new technique where the time required increases linearly with the number of atoms and, by using ‘K computer’ and the FX10 installed at Riken and the University of Tokyo, respectively, they successfully performed first-principles dynamical simulations of systems comprising more than 30,000 atoms. It paves the way for simulation of very large systems including up to millions of atoms. The results are published in the Journal of Chemical Theory and Computation.
Meanwhile, at the Argonne Leadership Computing Facility (ALCF) in the USA, researchers from the University of Illinois at Urbana-Champaign (UIUC) are using Mira, a 10-petaflops IBM Blue Gene/Q supercomputer, to simulate the magnetism of iron selenide, a known high-temperature superconductor, at varying levels of pressure. Their computational study was inspired by experimental work that found iron selenide becomes superconducting at high temperatures when pressure is applied.
Wagner received computing time at the ALCF through the US Department of Energy’s Office of Science Innovative and Novel Computational Impact on Theory and Experiment (INCITE) programme. He was awarded a second INCITE allocation in 2015 to continue his studies into high-temperature superconductors.
Wagner and his colleagues have developed the QWalk code, which they are running on Mira, to carry out quantum Monte Carlo (QMC) simulations of the structure of electrons in iron selenide at an unprecedented level of detail. Because superconducting materials are strongly correlated systems, predicting their behaviour is dependent on calculating the interactions between their electrons. Traditional computational methods, such as density functional theory, average these interactions out, which made it impossible to study such materials with any precision in the past.
However, with the increasing availability of high-performance supercomputers, the computationally demanding QMC method has emerged as an effective tool for explicitly simulating the interactions. By optimising the code, Wagner and his colleagues have been able to increase QWalk’s speed by 20 percent.