Revolutionary Advances in Computational Quantum Many Body Physics

Background: The predictive simulation of large-scale quantum effects in chemistry and materials science is a notoriously difficult topic in computational physics and mathematics. While exact solutions can be obtained for simplified and ad-hoc models, yielding useful verification data, the exact computation of the electronic structure of materials or complex molecules can still elude us, due to the exponentially large number of degrees of freedom (DOF) for N-body wave functions. Kohn- Sham density functional theory (DFT), a widely used and successful approach for estimating equilibrium properties, relies on the replacement of this many-body wave function by the electron density, and the minimization of a universal functional of this electron density to obtain the ground state. However, the form of this functional is unknown and the critical contributions of exchange and correlation energies must be modeled, sometimes with unpredictable results. Despite significant and recent progress, notably in accelerating DFT, the method faces challenges, e.g. for strongly-correlated systems, charge transfer reactions and multiple excitations. Other approaches are mostly based on stochastic sampling of the sparse many-body Hilbert space, i.e. quantum Monte Carlo (QMC), and are used to provide highly accurate, reference solutions, albeit at an extreme computational cost. Diagrammatic Monte Carlo, a more recent variation of QMC, is based on the random addition and cutting of graphs and the summation of weak-coupling diagrams up to a given order in the perturbation expansion. However, QMC can suffer from slow convergence due to stochastic noise, and this problem is amplified for low energy gaps between ground state excited states (critical slowing down). Another critical issue in these exact computations is the “sign problem” in the anti- symmetric ground state wave function of N-body fermions. This can potentially be handled in diagrammatic MC via near-cancellation of chosen diagrams, or by operator annihilation in a recently developed quantum MC method operating in the space of Slater determinants. Other approaches also of potential interest include quantum lattice Boltzmann models, lattice gauge theory and holographic duality. Rather than relying on disparate numerical approaches, we need a truly predictive design capability for quantum properties of realistic systems from first principles, along with their interaction with the environment. 

Objective: The long-term objective of this MURI will be to discover a universal approach to solving the many-body quantum physics for arbitrary configurations and dynamics, with predictive and quantifiable accuracy, and with sufficiently high performance to become an essential ab initio tool for mesoscale computations. This may require a totally new paradigm, or the integration of multiple approaches in mathematical, physical and engineering disciplines. 

Research Concentration Areas: Suggested research areas may include: (a) acceleration of DFT by several orders of magnitude; (b) theoretical development of QMC for strongly coupled systems; (c) exploration and exploitation of lattice-based methods, renormalization group, duality-based methods or dimensional projection; (d) non-stochastic kinetic equation solvers or dimensional reduction methods; (e) other innovative approaches for high-dimensional problems, including game theory and complex adaptive agents. Challenge problems must be defined and addressed, with systematic increase in system complexity, towards applications in realistic material science problems. Strongly correlated bosonic and fermionic systems (superfluids, superconductors) are of particular interest, along with both equilibrium and non-equilibrium, time-dependent properties of hybrid configurations. Only innovative, broadly applicable or integrated solutions, rather than isolated and/or incremental improvements, will be considered. 

Anticipated Resources: It is anticipated that awards under this topic will be no more than an average of $1.5M per year for 5 years, supporting no more than 6 funded faculty researchers. Exceptions warranted by specific proposal should be discussed with the topic chief during the white paper phase of the solicitation prior to submitting a full proposal. 

Research Topic Chiefs:

Dr. J.-L. Cambier, 703-696-1141 jean_luc.cambier@us.af.mil

Dr. T. Curcic, 703-696-6204 tatjana.curcic.1@us.af.mil

Dr. A. Sayir, 703-696-7236 ali.sayir.2@us.af.mil