Phase diagram and spin nematic phase transitions in biquadratic spin- 1 and spin-2 XY chains with single-ion anisotropies

We investigate quantum phase transitions between uniaxial (biaxial) spin nematic phases in biquadratic spin-1 (-2) XY infinite chains with the rhombic- and uniaxial-type single-ion anisotropies. The distinctive singular behaviors of the Wigner–Yanase skew information, the bipartite entanglement entropy, and the quadrupole moments characterize quantum phase transitions from one spin nematic state to another. For the spin-1 system, a discontinuous quantum phase transition is signaled by discontinuous behaviors of all the considered Wigner–Yanase skew information, bipartite quantum entanglement, and quadrupole moments from the z-ferroquadrupole phases to the x- or y-ferroquadrupole phases, while a continuous quantum phase transition occurs between the x- and y-ferroquadrupole phases. The central charge in the continuous phase transition line is estimated as c≃1 from the entanglement entropy. Compared to the spin-1 system, depending on a strength of the uniaxial-type single-ion anisotropy, the spin-2 system undergoes four different quantum phase transitions between the two biaxial spin nematic phases including quantum crossovers connecting the two orthogonal biaxial spin nematic states adiabatically without an explicit phase transition. 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 phase transition is advocated by the central charge c≃1. Whereas the continuous phase transition lines with c≃1/2 indicate that the transition between the biaxial spin nematic phase and the antiferromagnetic phase belongs to the Ising universality class.