We extend the nonlocality transfer matrix framework to quantum phases exhibiting spontaneous translational symmetry breaking. We show that for a broad family of these phases, the standard assumption—wherein the spatial periodicity of the transfer matrix ($u_T$) matches that of the ground state ($u$)—is insufficient to capture the maximal violation of Bell-type inequalities. Instead, we establish that an optimal construction with $u_T=2u$ is physically required to fully detect multipartite nonlocality in these regimes. Applying this generalized framework to the axial next-nearest-neighbor Ising model and the Kitaev-Heisenberg chain, we demonstrate that the extended nonlocality spectrum reveals multipartite nonlocality hidden by the conventional approach and provides sensitive signatures of quantum phase transitions.

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• Nonlocality
• Quantum correlations in quantum information
• Quantum correlations, foundations & formalism
• Quantum phase transitions
• 1-dimensional spin chains
• Tensor network methods