  We study ground state fidelity defined as the overlap between two ground
states of the same quantum system obtained for slightly different values of the
parameters of its Hamiltonian. We focus on the thermodynamic regime of the XY
model and the neighborhood of its critical points. We describe in detail cases
when fidelity is dominated by the universal contribution reflecting quantum
criticality of the phase transition. We show that proximity to the
multicritical point leads to anomalous scaling of fidelity. We also discuss
fidelity in a regime characterized by pronounced oscillations resulting from
the change of either the system size or the parameters of the Hamiltonian.
Moreover, we show when fidelity is dominated by non-universal contributions,
study fidelity in the extended Ising model, and illustrate how our results
provide additional insight into dynamics of quantum phase transitions. Special
attention is put to studies of fidelity from the momentum space perspective.
All our main results are obtained analytically. They are in excellent agreement
with numerics.
