Einstein-Podolsky-Rosen steering in critical systems

We explore Einstein-Podolsky-Rosen steering, measured by steering robustness, in the ground states of several typical models that exhibit a quantum phase transition. For the anisotropic XY model, steering robustness approaches zero around the critical point and vanishes in the ferromagnetic phase despite the fact that there exist other quantum nonlocalities, e.g. quantum entanglement. For the Heisenberg XXZ model, steering robustness exhibits some similar behavior as entanglement around the infinite-order quantum phase transition point Delta = 1, e.g. reaching its maximum. As a further example, we also consider steering robustness in the Lipkin-Meshkov-Glick collective spin model. It is then shown that steering robustness disappears at the transition point and remains at zero in the fully polarized symmetric phase, just like the behavior of entanglement and Bell nonlocality.