W-SLDA Toolkit

High-Performance Simulation Platform for Fermionic Superfluids

The W-SLDA Toolkit is a large-scale, high-performance computing (HPC) framework for solving mathematical problems formally equivalent to the Bogoliubov–de Gennes (BdG) equations and density functional theories for superfluid fermionic systems.

It enables self-consistent static and time-dependent simulations of:

• ultracold atomic Fermi gases,
• superconducting systems,
• atomtronical devices,
• strongly interacting fermionic matter,
• vortex dynamics and quantum turbulence,
• Josephson effects,
• impurity dynamics,
• spin- and mass-imbalanced superfluids.

The toolkit is optimized for execution on modern HPC systems and is designed for simulations involving thousands of particles on large 3D grids.

Scientific Scope

W-SLDA provides a unified numerical framework for:

• Bogoliubov–de Gennes (BdG) equations
• Superfluid Local Density Approximation (SLDA)
• Asymmetric SLDA (ASLDA)
• SLDA with extended terms (SLDAE)
• Custom user-defined energy density functionals

Both ground-state (static) and real-time (time-dependent) dynamics are supported in:

• 1D geometries,
• 2D geometries,
• full 3D Cartesian grids.

The code is particularly suited for studying emergent collective phenomena in strongly correlated fermionic systems.

Architecture Philosophy

W-SLDA follows a compile-time specialization model to maximize performance.

Users define the physical problem in C (external potentials, pairing fields, constraints, etc.) and build a dedicated executable optimized for the specific geometry and lattice size.

This approach:

• maximizes numerical performance,
• enables strong compiler optimizations,
• ensures scalability on HPC systems,
• promotes reproducible workflows.

The toolkit is designed as an open, extensible research platform for large-scale density-functional simulations of fermionic superfluids.

Reference

G. Wlazłowski, P. Magierski, M. M. Forbes, A. Bulgac,
W-SLDA Toolkit: A simulation platform for ultracold Fermi gases,
[arXiv:2602.08982].

If you use the W-SLDA Toolkit in your research, please cite the above work.

Official webpage

Repositories:

• Main repository (authoritative source): GitLab @ WUT
• Mirrors: GitLab, GitHub

Implemented Functionalities

• Solvers: static and time-dependent equations
• Dimensionality: 1D, 2D, and 3D geometries
• Energy density functionals: BdG, (A)SLDA, SLDAE, and user-defined custom functionals
• Temperature regimes: zero-temperature and finite-temperature calculations
• Spin configurations: spin-balanced and spin-imbalanced systems
• Mass imbalance: support for unequal particle masses
• External fields: user-defined external potentials, external pairing fields, external velocity fields, and time- and space-dependent scattering lengths
• Visualization: integration with the VisIt visualization tool
• Extensions: templates for data analysis workflows and a Python library for post-processing and data manipulation
• Accelerated convergence: Broyden mixing, automatic interpolations, and quantum friction techniques
• Template-based usage model
• Results reproducibility: built-in mechanisms for reproducible simulations
• Data format: support for the W-data format for storing simulation results

Main Codes

Static solvers:

• st-wslda-1d
• st-wslda-2d
• st-wslda-3d

Time-dependent solvers:

• td-wslda-1d
• td-wslda-2d
• td-wslda-3d

For a detailed description of the available code types, see Types of codes.

System Requirements

W-SLDA is designed for HPC environments.

Minimum requirements:

• C compiler (GCC, Intel, or equivalent)
• MPI implementation (OpenMPI, MPICH, or vendor-specific)
• FFTW
• ScaLAPACK
• BLAS/LAPACK
• Optional: ELPA (recommended for large-scale diagonalizations)
• Optional: CUDA or HIP compiler (for time-dependent calculations)

Recommended:

• Multi-node cluster environment
• High-memory nodes for 3D simulations
• GPU-enabled systems (if using GPU-enabled builds)

Installation and build instructions are available here.

Quick Start

Example: 1D static calculation.

1. Set environment variable:
   export WSLDA=/path/to/wslda

2. Create a working directory from a template:
   cp -r $WSLDA/st-project-template my-project-name

   Then enter the project directory:
   cd my-project-name

3. Edit the problem-definition files to configure your system:

   • predefines.h
   • problem-definition.h
   • logger.h
   • input.txt (edit before running the simulation)

4. Load required modules (example):
   source env.sh

5. Compile:
   make 1d

6. Run:
   mpirun -np 4 ./st-wslda-1d input.txt

An example demonstrating the full workflow (Josephson junction dynamics) from configuration to visualization is available here.

Documentation

For full documentation, usage examples, and tutorials, see the Wiki Pages.
Optionally, you can use wiki pages from mirror repositories: GitLab wikis, GitHub wikis.

Reproducibility and Data

W-SLDA supports structured output via the W-data format.

Reproducibility packs and benchmark examples are provided through the repository and official webpage.

License

W-SLDA Toolkit is distributed under the GNU General Public License v3 (GPLv3).

See the COPYING file for details.

Developers

For the complete list of developers and contributors, see Contributors.

Bug Reporting

To report bugs or issues:

• use the Issue tracking system
• or contact the development team via email: wslda@fizyka.pw.edu.pl

Contributing

If you would like to contribute to the W-SLDA Toolkit, please see the CONTRIBUTING.md file for guidelines and further information.