CERTIFY-ED: A Multi-Layer Verification Framework for Exact Diagonalization of Quantum Many-Body Systems

TL;DR

CERTIFY-ED is a comprehensive verification framework for exact diagonalization in quantum many-body physics, enhancing reliability through multi-layer validation, independent eigensolvers, and tamper-evident certificates.

Contribution

It introduces a multi-layer, multi-oracle verification system for ED results, integrated with existing packages, and includes tamper-evident certificates for result validation.

Findings

Successfully verifies 53 out of 53 unit tests and 81 out of 81 validation tests.

Maximum disagreement with QuSpin is 1.6×10⁻¹⁴ across 320 eigenvalue comparisons.

Agreement with high-precision references reaches 1.6×10⁻¹⁵.

Abstract

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