Quantum coherence as indicators of quantum phase transitions, factorization and thermal phase transitions in the anisotropic XY model

Quantifying quantum coherence has attracted considerable interests. In the present work, we employ two measures of quantum coherence recently proposed in terms of the skew information and the trace norm, respectively, to investigate the quantum phase transitions (QPTs), factorization in the XY model and the thermal phase transitions (TPTs) in the transverse field Ising model. Two quantifications of quantum nonlocality via the same distance measure of the quantum coherence are also studied for reference. It is shown that two types of quantum coherence are reliable in identifying QPTs and TPTs. However, only the quantum coherence based on the skew information can detect factorization. In addition, the quantum coherence and nonlocality measured via the same distance space have similar finite temperature scaling law, while the quantum coherence based on skew information and trace norm has different finite temperature scaling law. Moreover, the skew-information-based quantum coherence at finite temperature suggests that factorization vanishes when temperature exceeds 0.02 (Boltzmann constant \(k_{B} = 1\)), which is in agreement with the results of the fidelity for states with different distances of spin-pairs.