sparse-ir-fortran - A Fortran interface for sparse-ir

This library provides a Fortran interface for sparse-ir.

Installation

This package relies on the python package sparse-ir to generate the basis functions:

pip install sparse-ir[xprec]

Note, however, once the basis function are generated, this package is standalone. You can simply check out the repository and copy the relevant source files into your code directory:

git clone https://github.com/SpM-lab/sparse-ir-fortran

Documentation and tutorial

Check out our comprehensive tutorial, where self-contained notebooks for several many-body methods - GF(2), GW, Eliashberg equations, Lichtenstein formula, FLEX, ... - are presented. There is also a Fortran sample code.

Refer to the API documentation for more details on how to work with the Fortran library.

This library is currently somewhat restricted. There is also a fully fledged Python library and a Julia library available for the IR basis and sparse sampling.

Creating the basis functions

In order to work with sparse-ir-fortran, you first have to construct the basis functions. For this, you have two options: you can either create data files, which you load at runtime, or you can embed the data into a Fortran module itself.

Creating data files

1. Generate a data file:

   python dump.py 1e+4 1e-10 ir_nlambda4_ndigit10.dat
   

   This generates the data file ir_nlambda4_ndigit10.dat containing sparse sampling points and transformation matrices for Λ=10⁴ and ε=10^-10 (ε is a cut-off value used when creating IR-basis objects).

2. Build object files and link them to your program:

   gfortran  -c -o sparse_ir.o sparse_ir.f90
   gfortran  -c -o sparse_ir_io.o sparse_ir_io.f90
   

   You do not need sparse_ir_preset.f90 if your program reads a data file at runtime.

Embedding data in a Fortran source file

1. Generate a fortran source file: The following command generates a source file containg data for a matrix of Λ=10^nlambda (nlambda = 1, 2, 3, 4) and ε=10^-ndigit (ndigit = 10).

   python mk_preset.py --nlambda 1 2 3 4 --ndigit 10 > sparse_ir_preset.f90
   

2. Build object files and link them to your program: The generated file sparse_ir_preset.f90 is consistent with Fortran95 and can be compiled as follows:

   gfortran  -c -o sparse_ir.o sparse_ir.f90
   gfortran  -c -o sparse_ir_preset.o sparse_ir_preset.f90
   

   You do not need sparse_ir_io.f90 if your program uses embedded data.

How to use sparse-ir modules in your Fortran program

If your program reads data from the file, you should declare the use of the sparse-ir modules to initiate IR basis objects as follows:

program main
  use sparse_ir
  use sparse_ir_io

Or, if you want to use the embed data of IR basis objects, you should do this instead:

program main
  use sparse_ir
  use sparse_ir_preset

In either case, the derived type of "IR" should be declared.

  implicit none
  type(IR) :: ir_obj ! You can declare with any name you wish.

Hereafter it is assumed that you will set the parameters as Λ=10⁴, β=10³ and ε^-10. You can store the IR basis objects into the derived type of "IR" as follows:

Using sparse_ir_io:

  double precision :: beta ! inverse temperature
  ...
  beta = 1.0d3
  open(99, file="ir_nlambda4_ndigit10.dat", status='old') ! Any unit number is OK.
  ir_obj = read_ir(99, beta)

Using sparse_ir_preset:

  double precision :: beta ! inverse temperature
  ...
  beta = 1.0d3
  ir_obj = mk_ir_preset(4, 10, beta)

Here you are ready to use the IR basis objects and call the IR basis subroutines for a given value of beta in your program. If you want to use the IR basis sets with different values of beta, you can reset beta with using the subroutine set_beta:

  beta = 2.0d3
  call set_beta(ir_obj, beta)

This subroutine updates the objects depending on beta.

License and citation

This software is released under the Creative Commons Zero license. See LICENSE for details.

If you find the intermediate representation, sparse sampling, or this software useful in your research, please consider citing the following papers:

• Hiroshi Shinaoka et al., Phys. Rev. B 96, 035147 (2017)
• Jia Li et al., Phys. Rev. B 101, 035144 (2020)
• Markus Wallerberger et al., SoftwareX 21, 101266 (2023)

If you are discussing sparse sampling in your research specifically, please also consider citing an independently discovered, closely related approach, the MINIMAX isometry method (Merzuk Kaltak and Georg Kresse, Phys. Rev. B 101, 205145, 2020).