Spectral function and fidelity susceptibility in quantum critical phenomena

Abstract

In this paper, we derive a simple equality that relates the spectral function $I(k,ω)$ and the fidelity susceptibility $χ_F$, i.e. $% χ_F=\lim_{η\rightarrow 0}\fracπη I(0, iη)$ 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.

5 pages, 2 figures