Fidelity, dynamic structure factor, and susceptibility in critical phenomena

Motivated by the growing importance of fidelity in quantum critical phenomena, we establish a general relation between the fidelity and structure factor of the driving term in a Hamiltonian through the concept of fidelity susceptibility. Our discovery, as shown by some examples, facilitates the evaluation of fidelity in terms of susceptibility using well-developed techniques, such as density matrix renormalization group for the ground state, or Monte Carlo simulations for the states in thermal equilibrium.