Julia code to assert accuracy and regularizing properties of modified hamiltonian with blow up kinetic terms, as studied in [CHV]¹. It is a simple top layer over the plane-wave density functional theory package DFTK.jl².

Requirements:

Julia 1.8. and above.

Installing all dependancies

Open a Julia shell with julia --project in your local copy of this repository and call

using Pkg; Pkg.instantiate(".")

to install all the needed dependancies.

Usage

This code runs the computations to perform the numerical experiments from [CHV]¹ section 6.

To run the computations, first open the Julia shell with julia --project in your local copy of this repository and call include("launch_paper_computations.jl") to precompile the code. Two sets of general parameters are defined. The first one Test_parameters are used to test that the code didn't break. The second one Paper_parameters correspond to the parameters used in [CHV]¹.

From this point a simple call to the launch_computations function suffices to perform all numerical tests. Let us do a very rough (but fast) computation for face centered cubic crystaline silicon with PBE exchange correlation functional. Simply define an output directory with mkdir("../silicon_PBE") and call

launch_computations(silicon, blowup; Test_parameters..., output_dir="../silicon_PBE")

The code also supports graphene with PBE functional. Any other system can be added in deps/common/test_cases.jl by following the same syntaxe. Note that in the parameters, the arguments bandplot_res and single_band_res control the number of k-points respectively in the full band diagram and in the focus on a single band. The code uses basic finite-difference derivatives, which imposes to fix the parameters above 200 and 2000 respectively, to avoid numerical artifacts. The results of the paper are displayed for bandplot_res=300 and single_band_res=4000. Note that the process is time consuming for these parameters and have been run on a cluster.

Other files

All the files in deps/geometry are not related to the computations of [CHV]¹.

Contact

This is research code, not necessarily user-friendly, actively maintened or extremely robust. If you have questions or encounter problems, contact us at: Laurent(dot)vidal(at)enpc(dot)fr

Footnotes

1. E. Cancès, M. Hassan, L. Vidal: Modified-operator method for the calculation of band diagrams of crystalline materials (arXiv:2210.00442) ↩ ↩² ↩³ ↩⁴

2. https://github.com/JuliaMolSim/DFTK.jl ↩