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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2605.11787 |
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| _version_ | 1866917484317114368 |
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| author | Vehale, Sarang Goel, Ritu |
| author_facet | Vehale, Sarang Goel, Ritu |
| contents | Exact diagonalization (ED) is a workhorse technique in computational quantum many-body physics, but published ED results are rarely accompanied by machine-checkable evidence of their numerical correctness. The community typically relies on the implicit trust chain LAPACK $\to$ user code $\to$ result, with at most informal agreement against another package treated as confirmation. We argue that this practice is inadequate for a method whose output frequently underpins theoretical claims, and we present \textsc{certify-ed}, a verification framework designed to be used \emph{alongside} existing ED packages (QuSpin, XDiag, ALPS) rather than as a replacement for them. The framework consists of (i) a multi-oracle eigensolver that runs three independent LAPACK paths and reports their pairwise disagreement, (ii) thirteen logically independent validation layers covering algebraic invariants, analytic limits, alternative algorithms, arbitrary-precision reference computation, conservation laws, dynamical consistency, and finite-size scaling, and (iii) tamper-evident SHA-256 hashed certificates that downstream consumers can verify. The framework also ships an error-injection layer that confirms the entire pipeline detects six injected error classes. Running on sixteen physics models from one-dimensional spin chains to two-dimensional Kitaev honeycomb clusters, our reference implementation passes 53 of 53 unit tests and 81 of 81 individual validation tests in under thirty seconds, with maximum disagreement against QuSpin of $1.6\times 10^{-14}$ across 320 eigenvalue comparisons, and agreement with 50-digit \texttt{mpmath} reference values to $1.6\times 10^{-15}$. The package is released under the MIT license on Zenodo and Github |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11787 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | CERTIFY-ED: A Multi-Layer Verification Framework for Exact Diagonalization of Quantum Many-Body Systems Vehale, Sarang Goel, Ritu Strongly Correlated Electrons Computational Physics Exact diagonalization (ED) is a workhorse technique in computational quantum many-body physics, but published ED results are rarely accompanied by machine-checkable evidence of their numerical correctness. The community typically relies on the implicit trust chain LAPACK $\to$ user code $\to$ result, with at most informal agreement against another package treated as confirmation. We argue that this practice is inadequate for a method whose output frequently underpins theoretical claims, and we present \textsc{certify-ed}, a verification framework designed to be used \emph{alongside} existing ED packages (QuSpin, XDiag, ALPS) rather than as a replacement for them. The framework consists of (i) a multi-oracle eigensolver that runs three independent LAPACK paths and reports their pairwise disagreement, (ii) thirteen logically independent validation layers covering algebraic invariants, analytic limits, alternative algorithms, arbitrary-precision reference computation, conservation laws, dynamical consistency, and finite-size scaling, and (iii) tamper-evident SHA-256 hashed certificates that downstream consumers can verify. The framework also ships an error-injection layer that confirms the entire pipeline detects six injected error classes. Running on sixteen physics models from one-dimensional spin chains to two-dimensional Kitaev honeycomb clusters, our reference implementation passes 53 of 53 unit tests and 81 of 81 individual validation tests in under thirty seconds, with maximum disagreement against QuSpin of $1.6\times 10^{-14}$ across 320 eigenvalue comparisons, and agreement with 50-digit \texttt{mpmath} reference values to $1.6\times 10^{-15}$. The package is released under the MIT license on Zenodo and Github |
| title | CERTIFY-ED: A Multi-Layer Verification Framework for Exact Diagonalization of Quantum Many-Body Systems |
| topic | Strongly Correlated Electrons Computational Physics |
| url | https://arxiv.org/abs/2605.11787 |