\n\nWe apply the Wigner-Yanase skew information approach to analyze two typical models that exhibit a topological quantum phase transition. Based on the exact solutions of the ground states, the Wigner-Yanase skew information between two nearest sites for each of the two models is obtained. For the one-dimensional Kitaev chain model, the first-order derivative of the Wigner-Yanase skew information is non-analytical around the critical point. The scaling behavior and the universality are verified numerically. In particular, the skew information can also detect the factorization transition in such a model. For the two-dimensional Kitaev honeycomb model, the first-order derivative of the Wigner-Yanase skew information shows some singularities at the critical points where the system transits from the gapless phase to the gapped one. Our results suggest that the Wigner-Yanase skew information can serve as a good indicator of the topological phase transitions in these models and shed considerable light on the relationships between topological quantum phase transition and information theory.\n
We investigate the behaviors of Wigner–Yanase skew information and the l1 norm, as two different measures of quantum coherence, in a tripartite ground state of the anisotropic spin-1/2 XY model. Following the renormalization-group method, we analytically link the two measures with each other and with the ground state energy of the system. We demonstrate that both the quantities show distinctive behaviors at the critical point of the system. The analysis of the first derivatives of the quantities reveals nonanalyticity in their behaviors, capturing quantum phase transition. The scaling behavior of the system is analyzed and it is shown that the minimum of the first derivative of Wigner–Yanase skew information converges to zero and the maximum of the first derivative of l1 norm diverges and both approach to the critical point with increasing size of the system.
Quantum phase transitions (QPTs) between uniaxial or biaxial spin nematic (SN) phases are investigated in biquadratic spin-1 and spin-2 XY infinite chains with the rhombic- and uniaxial-type single-ion anisotropies. Systematic discussions of distinctive singular behaviors are made to classify various types of QPT from one SN state to the other SN state in using the Wigner-Yanase skew information (WYSI), the bipartite entanglement entropy (BEE), and the quadrupole moments (QMs). For the spin-1 system with the three uniaxial SN phases, we find that a discontinuous QPT, signaled by discontinuous behaviors of all the considered WYSI, BEE, and QMs, occurs from the z-ferroquadrupole phase (FQP) to the x- or y-FQPs, while a continuous QPT occurs between the x- and y-FQPs. The central charge in the continuous QPT line is estimated as
c≃1 from the BEE. Compared to the spin-1 system, depending on a given strength of the uniaxial-type single-ion anisotropy, the spin-2 system undergoes four different types of QPTs between the two biaxial SN phases as the rhombic-type anisotropy varies: the quantum crossovers, connecting the two orthogonal biaxial SN states adiabatically without an explicit phase transition, the continuous and the discontinuous QPTs, and the SN to magnetic transitions via the antiferromagnetic phase (AFP). In a sharp contrast to the spin-1 system, for the transitions between the two biaxial SN phases, the discontinuous transition line is classified as a topological phase characterized by a doubly degenerate entanglement spectrum and a string order parameter defined by the Cartan generator of the
SO(5) symmetry group in spin-2 systems, while the continuous QPT is advocated by the central charge
c≃1. Whereas the QPT lines with
c≃1/2 indicate that the transition between the biaxial SN phase and the AFP belongs to the Ising universality class.