Spectral function and fidelity susceptibility in quantum critical phenomena

In this paper, we derive a simple equality that relates the spectral function I(\mathbf{k},ω) and the fidelity susceptibility χ_F , i.e. χ_F=\lim_{η→ 0}\fracπη I(0, iη) with η being the half-width of the resonance peak in the spectral function. Since the spectral function can be measured in experiments by the neutron scattering or the angle-resolved photoemission spectroscopy (ARPES) technique, our equality makes the fidelity susceptibility directly measurable in experiments. Physically, our equality reveals also that the resonance peak in the spectral function actually denotes a quantum criticality-like point at which the solid state seemly undergoes a significant change.