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arXiv · 2606.19033

Contextuality as a Diagnostic of Translation-Symmetry Breaking in Translation-Invariant 1D Hamiltonians

Xiao Zeng·Kaiyan Yang·Lingxia Zhang·Zizhu Wang
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Abstract

Bell- and contextuality-type inequalities have become practical probes of many-body quantum correlations, often involving only few-body correlators and quantities with a direct Hamiltonian interpretation such as an energy density. Here we investigate the mechanism by which translation-invariant Hamiltonians generated from representative families of contextuality witnesses organize their ground-state structure in infinite one-dimensional systems. For the witness families considered, maximal quantum violation is realized by ground-state sectors with commensurate enlarged unit cells: the Hamiltonians are invariant under one-site translations, while the optimal ground states are $p$-periodic with $p>1$. At the corresponding classical-bound points, the ground-state sectors are highly degenerate and support many commensurate periods. Along the interpolation paths analyzed in this work, entering the contextual regime is accompanied by the lifting of this classical period degeneracy in favor of a quantum-selected period. We also identify finite periodic-boundary-condition benchmarks at the selected periods: for each model studied, the finite-ring witness reproduces the same classical bound and quantum value as the corresponding infinite-chain witness, and in several cases the resulting finite inequalities are tight. These reductions turn the infinite-chain contextuality certification into compact energy-estimation benchmarks requiring only local correlator measurements. We establish the mechanism analytically in representative two- and three-body witness models and corroborate it more broadly using translation-invariant semidefinite-program relaxations together with variational matrix-product-state calculations.

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Xiao Zeng, Kaiyan Yang, Lingxia Zhang, Zizhu Wang. 2026-08-11. Contextuality as a Diagnostic of Translation-Symmetry Breaking in Translation-Invariant 1D Hamiltonians. https://arxiv.org/abs/2606.19033

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