Criticality, factorization and Wigner–Yanase skew information in quantum spin chains

We apply the Wigner–Yanase skew information approach to analyze criticality and factorization phenomenon in the one-dimensional anisotropy \(XY\) model with uniform coupling interaction and periodic-two one. Based on the exact solutions of the ground states, the Wigner–Yanase skew information between two nearest-neighbor lattices is obtained. For the uniform case, the first-order derivative of the Wigner–Yanase skew information is non-analytically around the critical point. The scaling behavior and the universality are verified numerically. In particular, such skew information can also detect the factorization transition in this model. For the periodic-two case, it is found that there exist more than one phase-transition point in some parameter region due to the competition between periodicity and anisotropy. Furthermore, two kinds of phase transitions, i.e., the Ising and anisotropy transitions, driven by external field \(\lambda \) and the anisotropy parameter \(\gamma \), are investigated carefully by the skew information. Our results state that quantum phase transition driven by the anisotropy parameter \(\gamma \) can belong to the same universality class as the one driven by external field \(\lambda \).