Spectral function and fidelity susceptibility in quantum critical phenomena

Abstract

In this paper, we derive a simple equality that relates the spectral function $I(k,\omega )$ and the fidelity susceptibility ${\chi }_F$, i.e. 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.

5 pages, 2 figures

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• Counterdiabatic driving of the quantum Ising model
• Generalized fidelity susceptibility at phase transitions
• Imaginary-field-driven phase transition for the $2$D Ising antiferromagnet: A fidelity-susceptibility approach
• Evidence from on-site atom number fluctuations for a quantum Berezinskii-Kosterlitz-Thouless transition in the one-dimensional Bose-Hubbard model
• Adiabatic Sensing Enhanced by Quantum Criticality