In this work we evaluate quantum Fisher information (QFI) of a two-qubit reduced state in the Ising-XXZ diamond structure at finite temperatures, which is applied to demonstrate quantum criticality and quantum phase transition in this model. Here we adopt the average QFI with respect to the local orthonormal observable bases [Phys. Rev. A. 88, 014,301 (2013)]. The results show that QFI around quantum critical points decreases or increases steeper when the system temperature is relatively lower. Meanwhile the singularity of QFI’ first-derivatives is becoming more and more obvious as the temperature is approaching zero. By the finite-temperature QFI and its scaling relation with temperature, quantum phase transitions can be well detected from the entangled state in ferrimagnetic phase to an unentangled state in ferrimagnetic phase or to an unentangled state in ferromagnetic phase. Moreover it is further found that the two kinds of phase transitions can be distinguished by the different scaling behaviors. It has been proved that QFI has enough capability to characterize quantum phase transition at finite temperature.
The quantum Fisher information is of considerable interest not only for quantum metrology but also because it is a useful entanglement measure for finite temperature mixed states. In particular, it estimates the degree to which multipartite entanglement is present. Recent results have related the quantum Fisher information to experimentally measurable probes. While in principle possible, a direct evaluation of the quantum Fisher information at finite temperatures is technically challenging and here we show that a simple estimate can be obtained for materials where the single-mode approximation is valid. We focus on the
S=1 antiferromagnetic Heisenberg model with uniaxial anisotropy. Quantum Monte Carlo techniques are used to determine low-temperature correlations from which the quantum Fisher information can be estimated within the single-mode approximation. The quantum Fisher information is compared to the quantum variance for the staggered magnetization operators in the transverse direction and inequalities between the quantum Fisher information, the quantum variance, and the full variance are discussed. Both the quantum and full variance as well as the quantum Fisher information are examined at finite temperatures above the isotropic point and at the quantum critical point for the Haldane-N\'eel transition. A finite size scaling study of the quantum Fisher information is performed at the quantum critical point and used to confirm the Ising nature of the Haldane-N\'eel transition.