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ED2 (QS³-ED2)

Exact Diagonalization for Quantum Spin Systems

ED2 (QS³-ED2) is a Fortran-based Exact Diagonalization (ED) code for numerical studies of quantum spin lattice models. The project targets

  • reproducible research,
  • shared-memory performance via OpenMP,
  • minimal external dependencies.

Key features

  • General quantum spin Hamiltonians
    • Heisenberg / XYZ-type interactions
    • External magnetic fields
  • Controlled Hilbert-space truncation
    • Restriction by excitation number (e.g. number of spin-down states)
    • Efficient access to dilute or constrained sectors
  • Numerical solvers
    • Full diagonalization for very small systems
    • Lanczos-type iterative solvers for larger Hilbert spaces
  • Parallelization
    • Shared-memory parallelism via OpenMP
    • No MPI dependency (single-node execution model)
  • Linear algebra backends
    • BLAS/LAPACK (OpenBLAS, Intel MKL, or vendor implementations)

Documentation

Official documentation:

https://ed2.readthedocs.io/en/latest/

Includes:

  • Installation instructions
  • Quickstart examples
  • Input / output specifications
  • Reproducible reference examples
  • Validation benchmarks
  • Algorithmic background

Requirements

  • Linux (x86_64)
  • Fortran compiler
    • GNU Fortran (gfortran, GCC ≥ 10 recommended)
    • Intel oneAPI Fortran (ifort / ifx)
  • BLAS/LAPACK (OpenBLAS or Intel MKL)
  • OpenMP-capable compiler

Build & Installation (Autotools)

ED2 uses GNU Autotools.

git clone https://github.com/QS-Cube/ED2.git
cd ED2
autoreconf -vfi
./configure FC=ifort     # or FC=gfortran
make -j

BLAS/LAPACK:

  • OpenBLAS is detected automatically when available.
  • Otherwise Intel MKL is used as fallback (via -qmkl).

No PATH dependency is assumed for the ED2 executable.

Testing

Two test levels are provided.

Lightweight regression test

make check

Runs a minimal smoke test (ex1 only). This is intended to be fast and suitable for CI.

Extended regression suite

make check-long

Runs examples ex1–ex9 sequentially. This performs full physical workflows and may take longer.

check-long is intentionally implemented outside Automake’s test harness to improve robustness on HPC systems.

Directory layout

source/     Fortran source code
examples/   Reference physical examples
tests/      Regression tests (ex1–ex9)
tools/      Auxiliary scripts
docs/       Documentation sources

Reproducibility

For published results, please record:

  • QS³-ED2 version or Git commit hash
  • Compiler name and version
  • BLAS/LAPACK backend
  • OpenMP environment (OMP_NUM_THREADS etc.)
  • Input files

ED2 is designed so all examples can be reproduced from a clean git clone.

Citation

Before DOI assignment:

ED2 (QS³-ED2), QS-Cube/ED2, GitHub repository,
version <tag> or commit <hash>.

After DOI release, please use the Zenodo DOI.

A CITATION.cff file is provided.

License

MIT License. See LICENSE.

Authors and maintainers

  • Hiroshi Ueda
  • Daisuke Yamamoto

Contributing

Bug reports and pull requests are welcome.

For scientific usage, please ensure sufficient information is provided to guarantee reproducibility.