Multipartite nonlocality spectrum and quantum criticality in the one-dimensional infinite quantum model

Based on transfer matrix theory and the multipartite nonlocality spectrum {∣λ i ∣}, we systematically investigate ground-state nonlocal correlations across three canonical infinite, translationinvariant one-dimensional spin models, including the XXZ model, the three-body coupled Cluster- Ising model, and the Kitaev ladder model, which cover both conventional and topological quantum phase transitions (QPTs). We show that the emergence of multipartite nonlocal correlations can be quantitatively determined via the leading eigenvalue criterion ∣λ 1 ∣ > 1, offering a concise and reliable indicator for diagnosing nonlocal quantum features. Further numerical comparisons reveal that the leading eigenvalue ∣λ 1 ∣ is strongly model-dependent and lacks universal applicability for identifying quantum critical behaviors across different QPT types. In contrast, the nonlocality spectral gap Δ∣λ∣ = ∣λ 1 ∣ – ∣λ 2 ∣ exhibits prominent robustness against variations in system symmetry, coupling strength, and intrinsic transition mechanisms. It characterizes quantum criticality through three distinct response modes, thereby enabling a unified description of both conventional and topological QPTs. This work establishes the nonlocality spectrum as a versatile and powerful framework for the joint characterization of multipartite nonlocality and quantum criticality in one-dimensional many-body quantum systems.