Computing eigenpairs of quantum many-body systems with Polfed.jl
Abstract
We present Polfed$.$jl, an open-source Julia package implementing the Polynomially Filtered Exact Diagonalization (POLFED) algorithm for computing mid-spectrum eigenvalues and eigenvectors (shortly, eigenpairs) of quantum many-body Hamiltonians. Access to such eigenpairs is essential for studying non-equilibrium many-body physics, but is hindered by the exponential growth of Hilbert-space dimension. POLFED addresses this challenge through a polynomial spectral transformation evaluated on the fly within a Lanczos iteration, preserving Hamiltonian sparsity and substantially reducing memory costs compared to other diagonalization methods. The package supports flexible energy targeting, automatic optimization of the spectral mapping for structured Hamiltonians, and GPU acceleration, which is particularly effective since the dominant computational cost reduces to repeated sparse matrix-vector multiplications. Benchmarks on disordered spin-chain and fermionic models demonstrate access to larger system sizes than alternative approaches, and CPU--GPU comparisons confirm significant speedups. In particular, we also provide code for constructing the quantum sun model Hamiltonian, a toy model of a many-body ergodicity-breaking transition. While our focus is on many-body Hamiltonians, Polfed$.$jl may be applied to any large sparse matrix.
Related
- Second Law of Thermodynamics in Closed Quantum Many-Body Systems
- Bootstrapping symmetries in quantum many-body systems from the cross spectral form factor
- A Few Constrain Many: Correlation-Enhanced Learning of Many-Body Quantum Systems
- Restricted typicality in non-equilibrium quantum many-body systems
- Locally optimized variational evolution for quantum many-body systems
BibTeX
@misc{pintar2026computing,
title = {{Computing eigenpairs of quantum many-body systems with Polfed.jl}},
author = {Rok Pintar and Konrad Pawlik and Rafał Świętek and Miroslav Hopjan and Jan Šuntajs and Jakub Zakrzewski and Piotr Sierant and Lev Vidmar},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.10191},
eprint = {2605.10191},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.10191},
}
RIS
TY - UNPB
TI - Computing eigenpairs of quantum many-body systems with Polfed.jl
AU - Rok Pintar
AU - Konrad Pawlik
AU - Rafał Świętek
AU - Miroslav Hopjan
AU - Jan Šuntajs
AU - Jakub Zakrzewski
AU - Piotr Sierant
AU - Lev Vidmar
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2605.10191
UR - https://arxiv.org/abs/2605.10191
AB - We present Polfed$.$jl, an open-source Julia package implementing the Polynomially Filtered Exact Diagonalization (POLFED) algorithm for computing mid-spectrum eigenvalues and eigenvectors (shortly, eigenpairs) of quantum many-body Hamiltonians. Access to such eigenpairs is essential for studying non-equilibrium many-body physics, but is hindered by the exponential growth of Hilbert-space dimension. POLFED addresses this challenge through a polynomial spectral transformation evaluated on the fly within a Lanczos iteration, preserving Hamiltonian sparsity and substantially reducing memory costs compared to other diagonalization methods. The package supports flexible energy targeting, automatic optimization of the spectral mapping for structured Hamiltonians, and GPU acceleration, which is particularly effective since the dominant computational cost reduces to repeated sparse matrix-vector multiplications. Benchmarks on disordered spin-chain and fermionic models demonstrate access to larger system sizes than alternative approaches, and CPU--GPU comparisons confirm significant speedups. In particular, we also provide code for constructing the quantum sun model Hamiltonian, a toy model of a many-body ergodicity-breaking transition. While our focus is on many-body Hamiltonians, Polfed$.$jl may be applied to any large sparse matrix.
ER -