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.

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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)

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Documentation

Official documentation:

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

Includes:

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

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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

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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.

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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.

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Directory layout

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

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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.

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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.

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License

MIT License. See LICENSE.

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Authors and maintainers

• Hiroshi Ueda
• Daisuke Yamamoto

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Contributing

Bug reports and pull requests are welcome.

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