Locality classification of two-spin XXZ subsystem states

Determine, for two-spin reduced states of translation-invariant XXZ Hamiltonians parameterized by the correlators ⟨σ_xσ_x⟩ and ⟨σ_zσ_z⟩, which parameter values yield Bell-local correlations under all projective measurements; specifically, classify the full parameter space into local versus non-local regions beyond separability and CHSH-violation criteria.

Background

Ground states of XXZ spin models obey symmetries that constrain two-spin reduced states to a two-parameter family determined by ⟨σ_xσ_x⟩ and ⟨σ_zσ_z⟩. Prior results characterize separable versus entangled regions and identify where the CHSH inequality is violated, but CHSH non-violation does not imply locality. Thus, deciding which reduced states admit a local hidden-variable model for all projective measurements is a distinct and unresolved task.

Using their optimization framework, the authors analyze this parameter space and provide evidence that CHSH is nearly tight for these symmetries and that the physically realized boundary in one-dimensional XXZ models corresponds to local states. Nonetheless, the underlying classification problem was explicitly stated as open.