Magnetic-field-induced oscillation of multipartite nonlocality in spin ladders

Spin-1/2 two-leg ladder models under a magnetic field have a well-known phase diagram. In this paper, we use multipartite nonlocality (a measure of multipartite quantum correlations) to characterize the quantum correlations in the ladder models at zero temperature. Both finite-size and infinite-size ladders are considered. We investigate the global nonlocality S-g = S(vertical bar Psi(g)>), which describes quantum correlations of the ground states vertical bar Psi(g)> of the entire lattices, and the partial nonlocality S-p = S((rho) over cap (n)), which describes quantum correlations of the reduced states (rho) over bar (n) of some sublattices in the ladders. We find that as the magnetic field lambda increases, the global nonlocality S-g presents a single-peak curve. Moreover, the logarithmic measure ln S-g changes dramatically at the two critical fields lambda(c1) and lambda(c2) of the models and thus signals the quantum phase transitions in the models. For the partial nonlocality S-p, in the regions lambda(c1) < lambda < lambda(c2), we observe that the S-p(lambda) curve shows an oscillation. Numerical results reveal that the underling mechanism is the "major component transitions" in the reduced states (rho) over bar (n) of the sublattices. More importantly, the oscillation of the partial nonlocality S-p is modulated by the single-peak curve of the global nonlocality S-g. The result provides valuable clues about the relation between partial nonlocality and global nonlocality in low-dimensional quantum models.