Local quantum fisher information and quantum phase transitions in the XY spin-1/2 chain

We study the local quantum Fisher information (LQFI) of arbitrary two-qubit states for the anisotropic XY spin-1/2 chain in a transverse field h at finite temperature T. The results show that LQFI for the states of the nearest-neighbor and the next-nearest-neighbor spin pairs can clearly spotlight the critical point (CP)\(\gamma\) = 0 of a quantum phase transition (QPT) in this model even at finite T, due to the discontinuity of the first derivative of LQFI at \(\gamma\) = 0 (\(\gamma\) is the anisotropy parameter). Moreover, LQFI can successfully detect another QPT point h = 1 at T = 0, due to the divergence of the first derivative of LQFI at h = 1 if \(\left| \gamma \right| \ne 1\). When \(\left| \gamma \right| = 1\), the CP h = 1 can be also clearly detected by LQFI at T > 0. Besides, LQFI can pick out the special points (not the CPs), where LQFI always displays a cusp-like behavior. At some proper values of \(\gamma\) and h, LQFI can increase with increasing T as well. These remarkable properties suggest that LQFI could serve as an useful tool for experimentally detecting the CPs of QPTs in spin systems at finite T.