Multipartite nonlocality and topological quantum phase transitions in a spinless fermion quantum wire with uniform and incommensurate potentials

Multipartite nonlocality and Bell-type inequalities are used to characterize topological quantum phase transitions (QPTs) in a spinless fermion quantum wire, where both uniform potentials and incommensurate potentials are considered. First, the nonlocality measures show clear signals at the critical points in both the uniform model and the incommensurate model. It indicates that these QPTs are accompanied by dramatic changes of multipartite quantum correlations in the ground states. Second, finite-size scaling analysis is carried out. In particular, in the incommensurate model where translation invariance is broken, with some rescaling techniques, we successfully establish the scaling formula in the large-L limit. Finally, the full phase diagram of the model with mixed potentials is figured out. We find a region which is featured with strong randomness in the large-L limit. The structure of this region is revealed by analyzing the energy spectrum, and an efficient approach to characterize this region is proposed.