Bell nonlocality in conventional and topological quantum phase transitions

Abstract

We investigate the critical behaviors of the Bell nonlocality, which are measured by the Bell-function values, in conventional and topological quantum-phase transitions. First, by using the quantum-renormalization-group method, we show that the Bell function value of a three-qubit Bell inequality in the anisotropic spin-1/2 XY model exhibits singular behaviors at the critical point. Moreover, for topological quantum-phase transitions, we find that the first-order derivative of the Bell-function value of the well-known Clauser-Horne-Shimony-Holt inequality in the Kitaev-Castelnovo-Chamon model behaves singularly at the topological-phase-transition point. Our results have established a link between quantum nonlocality and phase transitions. © 2012 American Physical Society.