Quantum coherence and spin nematic to nematic quantum phase transitions in biquadratic spin-1 and spin-2 XY chains with rhombic single-ion anisotropy

We investigate quantum phase transitions and quantum coherence in infinite biquadratic spin-1 and -2 XY chains with rhombic single-ion anisotropy. All considered coherence measures such as the l(1) norm of coherence, the relative entropy of coherence, and the quantum Jensen-Shannon divergence, and the quantum mutual information show consistently that singular behaviors occur for the spin-1 system, which enables to identify quantum phase transitions. For the spin-2 system, the relative entropy of coherence and the quantum mutual information properly detect no singular behavior in the whole system parameter range, while the l(1) norm of coherence and the quantum Jensen-Shannon divergence show a conflicting singular behavior of their first-order derivatives. Examining local magnetic moments and spin quadrupole moments lead to the explicit identification of novel orderings of spin quadrupole moments with zero magnetic moments in the whole parameter space. We find the three uniaxial spin nematic quadrupole phases for the spin-1 system and the two biaxial spin nematic phases for the spin-2 system. For the spin-2 system, the two orthogonal biaxial spin nematic states are connected adiabatically without an explicit phase transition, which can be called quantum crossover. The quantum crossover region is estimated by using the quantum fidelity. Whereas for the spin-1 system, the two discontinuous quantum phase transitions occur between three distinct uniaxial spin nematic phases. We discuss the quantum coherence measures and the quantum mutual information in connection with the quantum phase transitions including the quantum crossover.

Automated summary

In this study, quantum phase transitions and coherence in infinite biquadratic spin-1 and -2 XY chains with rhombic single-ion anisotropy were investigated. Singular behaviors were identified in the spin-1 system using coherence measures, while the spin-2 system did not exhibit singular behavior in the parameter range. Novel orderings of spin quadrupole moments with zero magnetic moments were found in both systems. Adiabatic connections between orthogonal biaxial spin nematic states in the spin-2 system were observed without explicit phase transitions, while discontinuous quantum phase transitions occurred between distinct uniaxial spin nematic phases in the spin-1 system. Discussions on quantum coherence measures and quantum mutual information in connection with quantum phase transitions including the quantum crossover were also provided.