Probing Strong Correlations with Light Scattering: the Example of the Quantum Ising model

In this paper we calculate the nonlinear susceptibility and the resonant Raman cross section for the paramagnetic phase of the ferromagnetic Quantum Ising model in one dimension. In this region the spectrum of the Ising model has a gap $m$. The Raman cross section has a strong singularity when the energy of the outgoing photon is at the spectral gap $\omega_{f} \approx m$ and a square root threshold when the frequency difference between the incident and outgoing photons $\omega_{i} -\omega_{f} \approx 2m$. The latter feature reflects the fermionic nature of the Ising model excitations.