Quantum Coherence And Phase Transitions In Spin Nematic Systems

Quantum phase transition is one of the major research topic of condensed matter physics.And the low-dimensional quantum system is particularly importa nt for the strange phenomenon it shows near the critical points.In the same ti me the development of quantum information theory also provides a series of ne w perspectives to investigate quantum phase transition.Among them the relation between quantum coherence and quantum phase transition attracts many research interests since recent researches have shown the deep relationship between quant um phase transition and the quantum coherence and many new physics have bee n revealed though such investigation.Yet the computing complexity of the stron g-correlated system makes it nearly impossible to get an analytical solution of gi ven Hamiltonian of particular system.Thus numerical simulation approach has t hen became major method in recent studies of quantum many-body system.Ma ny numerical simulation algorithms have been developed according to the newly progress of computer science recently.And the tensor network based on matrix product states and the infinite time-evolving block decimation method which are applied in our research are among them.In this study,we investigate quantum phase transitions and quantum coherence i n infinite biquadratic spin-1 and-2 XY chains with rhombic single-ion anisotropy.All considered coherence measures such as the7)₁ norm of coherence,the relative e ntropy of coherence,and the quantum Jensen-Shannon divergence,and the quantum mutual information show consistently that singular behaviors occur for the spin-1 s ystem,which enables to identify quantum phase transitions.For the spin-2 system,the relative entropy of coherence and the quantum mutual information properly dete ct no singular behavior in the whole system parameter range,while the7)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 spi n quadrupole moments lead to the explicit identification of novel orderings of spin quadrupole moments with zero magnetic moments in the whole parameter space.W e 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,t he two orthogonal biaxial spin nematic states are connected adiabatically without an explicit phase transition,which can be called quantum crossover.The quantum cro ssover region is estimated by using the quantum fidelity.Whereas for the spin-1 sy stem,the two discontinuous quantum phase transitions occur between three distinct uniaxial spin nematic phases.We then introduced full width at half maximum me thod and determined the quantum crossover region.