  An innovative test for detecting quantum chaos based on the analysis of the
spectral fluctuations regarded as a time series has been recently proposed.
According to this test, the fluctuations of a fully chaotic system should
exhibit 1/f noise, whereas for an integrable system this noise should obey the
1/f^2 power law. In this letter, we show that there is a family of well-known
integrable systems, namely spin chains of Haldane-Shastry type, whose spectral
fluctuations decay instead as 1/f^4. We present a simple theoretical
justification of this fact, and propose an alternative characterization of
quantum chaos versus integrability formulated directly in terms of the power
spectrum of the spacings of the unfolded spectrum.
