[Under construction]

2017 AFOSR MURI

PO: Dr. Fariba Fahroo, Computational Mathematics

PI: Garnet Kin-Lic Chan, California Institute of Technology

MURI Website

In this MURI, we will advance the computational methods of chemistry, physics, and materials science along two fronts (i) to confidently treat the quantum many-body physics of systems with strong electronic correlations, and (ii) to carry out fast simulations of non-periodic materials with structural complexity across hundreds of thousands of atoms.

The first class of systems, namely strongly correlated electron materials, provide the most stunning examples of large-scale quantum effects, with exotic quantum phases ranging from high temperature superconductivity to strange metals and fractional quantum Hall states. It is a longstanding holy grail of computational quantum many-body physics to describe these correlations directly from the many-particle Schrödinger equation. In the last two decades, important new ideas about the structure of electronic correlations have emerged through new renormalization group methods (RG), tensor network states (TNS), and new forms of quantum Monte Carlo (QMC). In this proposal, we combine the ideas of RG, TNS, and QMC, with the latest advances in first principles materials simulation, to make a concerted push that will enable us to carry out the first realistic and fully ab-initio simulations of strongly correlated electronic materials.

The second class of systems are complex non-periodic materials. Many real problems of interest, with defects, surfaces, or more complicated 3D structures, do not possess simple lattice translational vectors. We will focus on the two kinds of non-periodic systems that can be mathematically described without disorder averaging. The first kind is one where the perturbation to the periodic structure is confined to a local region. This includes materials with structural defects, electronic impurities, as well as boundaries such as surfaces. To describe these problems we will pursue the formalism of Green’s function quantum embedding, where defects appear as natural mathematical objects. The second kind are those where atoms are related not by translation vectors, but by more general isometries: these are mathematically described by the theory of objective structures. In this proposal, we advance new mathematical ideas for fast density functional methods, within the formalism of Green’s function quantum embedding and the theory of objective structures, to develop modeling capabilities for non-periodic bulk and low dimensional materials where structural complexity is expressed over hundreds of thousands of atoms.

While our proposed work develops new computational algorithms for quantum many-body chemistry and physics, we will concentrate and focus our efforts through real materials challenges. In the course of the funded work, we will carry out two landmark simulations that simply would not be conceivable without the combined advances of the different research efforts in the MURI. The first will be to perform a fully correlated simulation of a bulk correlated electronic material, for the first time, to understand the origins of exotic phases such as high temperature superconductivity. The second will be to calculate the electronic properties of general twisted multilayer 2D materials, opening up the possibility to search for new multilayer materials with tailored electronic and optical properties. These simulations will alter the landscape of modern materials modeling, in terms of both the complexity of the quantum many-body phenomenology that can be described, and the complexity of the atomic composition.