Revealing divergent length scales in the Kitaev honeycomb model with quantum Fisher information.

Quantum Fisher information (QFI) is a concept from quantum metrology
that has gained extensive recent application to condensed matter physics, pri-
marily because it is easily accessible in neutron scattering experiments and can
be used to quantify the amount of multipartite entanglement in a system at
finite temperatures. We present results for the QFI in the Kitaev honeycomb
model (KHM), where the derivatives of the QFI with respect to the driving
parameter detect the presence of the gapped-gapless phase transition by. We
compute the scaling of the divergence of the second derivatives of the QFI on the approach to the critical
point, and show that the diverging QFI can be understood in terms of diverg-
ing length scales in the two point correlation functions for the site and bond
magnetization operators. In the former case, this correlation length is the two
point correlator of the Majorana degrees of freedom.