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Green/Continuation is an Analytical continuation toolkit for Green Software Package
Installation
Green/Continuation comes in two forms
- C++ application
- Python package
Dependencies
Green/Continuation has the following required external dependencies
- HDF5 library version >= 1.10.2
- Message Passing Interface >= 3.1 (for C++ application)
- Eigen3 library >= 3.4.0
- GNU Multiprecision library
- pybind11 (optional to build python wrapper)
To build Green/Continuation CMake version 3.18 or above is required
Build and Install C++ application
The following example will build, test and install Green/Continuation to /path/to/weakcoupling/install/dir directory.
$ git clone https://github.com/Green-Phys/green-ac
$ cd green-ac
$ mkdir build && cd build
$ cmake -DCMAKE_BUILD_TYPE=Release \
-DCMAKE_INSTALL_PREFIX=/path/to/install/dir ..
$ make
$ make test
$ make install
Installation of Python package
We provide pre-built binaries for major Linux distributions and recent MacOS version via pip.
For installation using pip simply type pip install green-ac.
If pre-built binaries can not be used, package will be built from sources.
Usage
C++ application
After the Green/Continuation is built and installed, spectral function could be obtained by calling
<install dir>/bin/ac.exe --BETA <Inverse temperature> --grid_file <grid file> \
--input_file <input file> --output_file <output file> --group <HDF5 group with data> \
--e_min -5.0 --e_max 5.0 --n_omega 4000 --eta 0.01 \
--kind Nevanlinna
BETA-- the inverse temperature that was used to obtain resultsgrid_file-- name of the grid file that was used to obtain resultsinput_file-- name of the file that contains imaginary time dataoutput_file-- name of the file to store results of the continuationgroup-- name of the group that containsdataandmeshdatasets with imaginary time data and gride_min-- lowest frequency on the real axise_max-- largest frequency on the real axisn_omega-- number of frequency points on the real axiseta-- broadening parameterkind-- type of continuation to be used (current version only supportsNevanlinna)
After the completetion, results will be stored in group HDF5 group in the output_file file.
Python
In addition to C++ application, Green/Continuation provides a convinient Python package that can work directly with
numpy arrays. It supports two types of parallelism, using ProcessPoolExecutor from concurrent.futures and
MPI parallelization using mpi4py library.
To use Green/Continuation simply import it in your script as
import green_ac
and call solve function with the following parameters:
- Type of the continuation (currently we only provide
Nevanlinna) - Matsubara frequency grid
- Real frequency grid
- Data in Matsubara frequency domain
- Precision
Here is an example how to obtain real frequency Green's function for a simple two-pole non-interacting Green's function with precision at least 512 bits:
imgrid = (2*np.linspace(-50,49,100) + 1) * 1.j *np.pi/ 2
grid = np.linspace(-2,2,1001) + 0.01j
data = 0.5*(1/(imgrid + 0.5) + 1/(imgrid - 0.5))
data_out = green_ac.solve("Nevanlinna", imgrid, grid, data, 512)
Here we have 100 positive and negative Matsubara frequencies, define real frequency grid to have 1000 points and to be from -2 to 2 with broadening parameter 0.01,
We define Green's function on Matsubara grid with poles at -0.5 and 0.5. Real frequency data will be stored in data_out array.
Acknowledgements
This work is supported by National Science Foundation under the award OCA-2310582
1 maintainer
Metadata
1 maintainer
Release files for green-ac 0.2.8
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