  We derive a general formula of the reduced fidelity susceptibility when the
reduced density matrix is $2\times2$ block-diagonal. By using this result and
the continuous unitary transformations, we study finite-size scaling of the
reduced fidelity susceptibility in the Lipkin-Meshkov-Glick Model. It is found
that it can be used to characterize quantum phase transitions, implying that we
can extract information of quantum phase transitions only from the fidelity of
a subsystem, which is of practical meaning in experiments.

Quantum Physics