Efficient and accurate Dynamical Mean Field Theory on the cloud

May, 2021

As part of project Quantifi, an Innovate UK funded project, Rahko, Johnson Matthey, and Amazon Web Services (AWS), have jointly demonstrated the use of high-performance computing (‘HPC’) to deliver efficient and accurate Dynamical Mean Field Theory (‘DMFT’) calculations on the cloud. 

 

Discovery of non-conventional materials 

Strongly correlated materials are a type of quantum materials that show unusual electronic and magnetic properties, such as metal-insulator transitions, heavy fermion behavior, half-metallicity, and spin-charge separation. These special properties can be utilized in various applications such as in field effect transistors, superconducting magnets, and magnetic storage devices contributing to the development of computers, scientific instruments, and other electronic devices.

The in silico design of such materials requires theoretical methods that take into account the strong static correlation that determines the electronic structure of these materials. However, standard mean field methods, for example, approximate density functional theory (‘DFT’) methods cannot fully capture these quantum effects, viz. that electronic behaviour in these materials cannot be effectively described in terms of non-interacting particles.

DMFT is a successful method that overcomes this problem by mapping the generally intractable many-body lattice problem to a local impurity model whose solution is already feasible. 

 

The Advantage of DMFT over DFT

The applicability of DMFT to non-conventional materials can be demonstrated for example by SrVO3, which is a prototypical strongly correlated metal, well-investigated because of its simple perovskite structure, and an interesting system for multiple reasons.

According to the experiments, the width of the t2g band is expected to be around 1.3 eV. DFT approximations predict this band considerably wider for example to be 2.6 eV by the local density approximation. While DMFT can reproduce the experimentally derived bandwidth quite well.

Also in accordance with the experiments, an upper and a lower satellite feature can be observed with DMFT that were initially identified as Hubbard bands but later explained in terms of plasmonic excitations.

Figure 1. DMFT band structure for SrVO3 lattice

 

Scaling of DMFT on AWS

The test calculations used an integrated DMFT software for correlated electrons (DCore), together with the continuous-time hybridization-expansion (CTHYB) quantum Monte Carlo solver, available in the Toolbox for Research on Interacting Quantum Systems (TRIQS). These test calculations were performed in an HPC environment on AWS designed in collaboration with the Amazon Quantum Solutions Lab team using AWS ParallelCluster.

These test calculations demonstrated that 91% parallelization can be achieved on multiple 36-core c5n.18xlarge nodes with the Linear Algebra Package (LAPACK) and the Intel Message Passing Interface (IntelMPI) for the relatively small bulk SrVO3 with five atoms in the unit cell. This parallelization is expected to be even higher for larger systems.

This implementation has been a valuable addition to Hyrax, Rahko’s quantum discovery platform. Hyrax also includes a version of DMFT able to run on current generation Quantum Computers (see DMFT on Quantum Computers).

 

Figure 2. Strong scaling results on SrVO3 lattice