  We study the fidelity susceptibility of quantum antiferromagnetic Ising chain
with a long-range power law interaction $1/r^{\alpha}$ using the large-scale
density matrix renormalization group method. We find that the critical
adiabatic dimension $\mu=2$ and the critical exponent of the correlation length
$\nu=1$ for arbitrary $\alpha>0$, indicating all quantum phase transitions are
second-order Ising transitions. In addition, we numerically determine the
complete phase diagram for $0 < \alpha \le 3$ from the data collapse of the
fidelity susceptibility and show that the critical point $h_c$ changes
monotonously with respect to $\alpha$. This work will shed light on the nature
of phase transitions in the quantum long-range antiferromagnetic Ising chain
from a quantum information perspective.
