  The notion of fidelity in quantum information science has been recently
applied to analyze quantum phase transitions from the viewpoint of the ground
state (GS) overlap for various many-body systems. In this work, we unveil the
intrinsic relation between the GS fidelity and the derivatives of GS energy and
find that they play equivalent role in identifying the quantum phase
transition. The general connection between the two approaches enables us to
understand the different singularity and scaling behaviors of fidelity
exhibited in various systems on general grounds. Our general conclusions are
illustrated via several quantum spin models which exhibit different kinds of
QPTs.
