self_consistency_solver

Contact: Matthias Stosiek, Department of Applied Physics, Aalto University, [email protected]

The Python modules in the folder /Modules/ contain different versions of a self-consistency solver all containing a full diagonalization (for number of moments Nm=0) and Kernel Polynomial Method solver (for Nm>0). The full diagonalization solver is the same in every module.

1. The KPM solver of "self_consistency_MatrixFree_bdg.py" contains an optimized matrix-free sparse matrix product (written in C) that only works with TR- and PH- symmetric s-wave superconductors as outlined in our publication.
2. The KPM solver of "self_consistency_MKL_bdg.py" contains a MKL sparse matrix product (python wrapper and polynomial expansion written by Dominik Hahn) that can be used for any Hamiltonian. To use this solver for a different system than the implemented one, the self-consistency equations, Hamiltonian and details of the polynomial expansion have to be adjusted.
3. The KPM solver of "self_consistency_AllInPython_bdg.py" is written entirely in Python but very slow for that reason.
4. The KPM solver of "self_consistency_RandomTraceEvaluation_bdg.py" uses a Random Trace Evaluation approach but needs optimization to be practical.

We have applied the self-consistency solver to various problems in disordered superconductors, see
M. Stosiek, B. Lang, and F. Evers, Phys. Rev. B 101, 144503 (2020)
M. Stosiek, F. Evers, and I. S. Burmistrov, Phys. Rev. Research 3, L042016 (2021)
M. Stosiek, C. Baretzky, T. Balashov, F. Evers, and W. Wulfhekel, Phys. Rev. B 105, L140504 (2022)
M. Lizée, M. Stosiek, I. Burmistrov, T. Cren, and C. Brun, Phys. Rev. B 107, 174508 (2023)

Compilation (only necessary for 1. and 2.)

1. In the folder "/chebyshev_matrixfree" in the file "chebyshev_final_icc_double.c" determine the linear dimension of the system with the variable N and the number threads with the variable NrndVec. Then execute make in folder "/chebyshev_matrixfree". The number of threads needs to be set accordingly in /Modules/self_consistency_MatrixFree_bdg.py. The number of threads Nthreads that will be used for full diagonalization solvers and the Hamiltonian rescaling can be set with MKL_NUM_THREADS=Nthreads and OMP_NUM_THREADS=Nthreads. Append /Modules to LD_LIBRARY_PATH.
2. In the folder "/chebyshev_matrix" execute make. The number of threads Nthreads can be set with MKL_NUM_THREADS=Nthreads and OMP_NUM_THREADS=Nthreads. Append /Modules to LD_LIBRARY_PATH. In both the Makefile and cy_parallel.sh the paths for the Python and Numpy headers and Python libraries must be set.

Usage

Example job scripts are given with "start_self_consistency_solver.py" and "start_self_consistency_solver_MKL.py" for codes 1. and 2. respectively.

Start the script with:

python start_self_consistency_solver.py folder startfile system_size

In "folder" the self-consistent-fields will be written and read in every step. If the code has been stoppen before self-consistency was reached, it automatically restarts at the most recent iteration, if "folder" contains a file with the correct parameters and filename. Each file is designated a separate random number seed. In the same file a close parameter configuration (in temperature, interaction strength, disorder strenght, number of Chebyshev moments or particle density) is searched for as a starting guess for the self-consistency solver. With "startfile" the first numbered suffix of the output filenames is defined. All the following output files will be numbered as defined in the script. "system_size" defines the linear system size of the square lattice

All other parameters temperature, disorder strength, number of Chebyshev moments, particle density etc. are determined within the job scripts.

Terms of Use

When using the self-consistency solver, please acknowledge the usage and cite the following work: M. Stosiek, B. Lang, and F. Evers, Phys. Rev. B 101, 144503.