Accurate, scalable computations in many-electron systems

One of the grand challenges in materials physics and chemistry is the accurate treatment of interacting many-electron systems. Computational methods need to reach beyond the incredible success afforded by the Kohn-Sham density functional theory (KS-DFT), and its independent-electron and perturbative extensions. This is difficult because of the combinatorial growth of the dimension of the Hilbert space involved, along with the high degree of entanglement produced by the combination of Fermi statistics and electron-electron interactions. Progress in addressing this challenge will be fundamental to the realization of “materials genome” or materials by design initiatives. Recently, significant advances have been achieved by the combination of methodological and algorithmic developments with petascale computing, which has lead to the solution of a number of challenging problems. I will give a brief overview of these advances, and then discuss one of the computational frameworks that have played an important role in them, the auxiliary-field quantum Monte Carlo method. The framework can be viewed as a superposition of KS-DFT systems evolving in fluctuating auxiliary fields, which are treated by stochastic sampling. The approach has demonstrated excellent accuracy across a wide range of quantum many-electron systems; it has computational complexity that scales as a low polynomial of the number of electrons; and it is ideally suited for high-performance computing platforms. A few illustrative examples will be discussed from recent applications in physics and chemistry.