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

TL;DR

This paper investigates the nonlinear optical response of the one-dimensional quantum Ising model in its paramagnetic phase, revealing singularities linked to its fermionic excitations and spectral gap.

Contribution

It provides the first calculation of nonlinear susceptibility and resonant Raman cross section for the quantum Ising model in this phase.

Findings

Raman cross section exhibits a strong singularity at the spectral gap.

A square root threshold appears at twice the spectral gap.

Features reflect the fermionic nature of excitations.

Abstract

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.