Spectral function and fidelity susceptibility in quantum critical phenomena

TL;DR

This paper establishes a direct link between spectral functions measurable in experiments and fidelity susceptibility, providing a new way to detect quantum criticality through experimental techniques like neutron scattering and ARPES.

Contribution

It derives a simple equality connecting spectral function and fidelity susceptibility, enabling experimental measurement of quantum critical phenomena.

Findings

Fidelity susceptibility can be obtained from spectral function measurements.

Resonance peaks in spectral functions indicate quantum critical points.

The equality bridges theoretical concepts with experimental observables.

Abstract

In this paper, we derive a simple equality that relates the spectral function $I(k,\omega)$ and the fidelity susceptibility $\chi_F$, i.e. $% \chi_F=\lim_{\eta\rightarrow 0}\frac{\pi}{\eta} I(0, i\eta)$ with $\eta$ 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.