Title: A domain-specific language and matrix-free stencil code for investigating electronic properties of Dirac and topological materials,
Abstract: We introduce PVSC-DTM (Parallel Vectorized Stencil Code for Dirac and
Topological Materials), a library and code generator based on a domain-specific
language tailored to implement the specific stencil-like algorithms that can
describe Dirac and topological materials such as graphene and topological
insulators in a matrix-free way. The generated hybrid-parallel (MPI+OpenMP)
code is fully vectorized using Single Instruction Multiple Data (SIMD)
extensions. It is significantly faster than matrix-based approaches on the node
level and performs in accordance with the roofline model. We demonstrate the
chip-level performance and distributed-memory scalability of basic building
blocks such as sparse matrix-(multiple-) vector multiplication on modern
multicore CPUs. As an application example, we use the PVSC-DTM scheme to (i)
explore the scattering of a Dirac wave on an array of gate-defined quantum
dots, to (ii) calculate a bunch of interior eigenvalues for strong topological
insulators, and to (iii) discuss the photoemission spectra of a disordered Weyl
semimetal.