Spectral function and fidelity susceptibility in quantum critical phenomena

Abstract

In this paper, we derive a simple equality that relates the spectral function\n$I(k,\\omega)$ and the fidelity susceptibility $\\chi_F$, i.e. $%\n\\chi_F=\\lim_{\\eta\\rightarrow 0}\\frac{\\pi}{\\eta} I(0, i\\eta)$ with $\\eta$ being\nthe half-width of the resonance peak in the spectral function. Since the\nspectral function can be measured in experiments by the neutron scattering or\nthe angle-resolved photoemission spectroscopy(ARPES) technique, our equality\nmakes the fidelity susceptibility directly measurable in experiments.\nPhysically, our equality reveals also that the resonance peak in the spectral\nfunction actually denotes a quantum criticality-like point at which the solid\nstate seemly undergoes a significant change.\n