One of the most promising techniques used for studying the electronic properties of materials is based on Density Functional Theory (DFT) approach and its extensions. DFT has been widely applied in traditional solid state physics problems where periodicity and symmetry play a crucial role in reducing the computational workload. With growing compute power capability and the development of improved DFT methods, the range of potential applications is now including other scientific areas such as Chemistry and Biology. However, cross disciplinary combinations of traditional Solid-State Physics, Chemistry and Biology drastically improve the system complexity while reducing the degree of periodicity and symmetry. Large simulation cells containing of hundreds or even thousands of atoms are needed to model these kind of physical systems. The treatment of those systems still remains a computational challenge even with modern supercomputers. In this paper we describe our work to improve the scalability of Quantum ESPRESSO [1] for treating very large cells and huge numbers of electrons. To this end we have introduced an extra level of parallelism, over electronic bands, in three kernels for solving computationally expensive problems: the Sternheimer equation solver (Nuclear Magnetic Resonance, package QE-GIPAW), the Fock operator builder (electronic ground-state, package PWscf) and most of the Car-Parrinello routines (Car-Parrinello dynamics, package CP). Final benchmarks show our success in computing the Nuclear Magnetic Response (NMR) chemical shift of a large biological assembly, the electronic structure of defected amorphous silica with hybrid exchange-correlation functionals and the equilibrium atomic structure of height Porphyrins anchored to a Carbon Nanotube, on many thousands of CPU cores.

No abstract

We have developed an application and implemented parallel algorithms in order to provide a computational framework suitable for massively parallel supercomputers to study the unitary dynamics of quantum systems. We use renowned parallel libraries such as PETSc/SLEPc combined with high-performance computing approaches in order to overcome the large memory requirements to be able to study systems whose Hilbert space dimension comprises over 9 billion independent quantum states. Moreover, we provide descriptions on the parallel approach used for the three most important stages of the simulation: handling the Hilbert subspace basis, constructing a matrix representation for a generic Hamiltonian operator and the time evolution of the system by means of the Krylov subspace methods. We employ our setup to study the evolution of quasidisordered and clean many-body systems, focussing on the return probability and related dynamical exponents: the large system sizes accessible provide novel insights into their thermalization properties.