Dynamical susceptibility near a long-wavelength critical point with a nonconserved order parameter*

Many strongly correlated electronic systems evince long-wavelength phase transitions, such as nematic transitions. The dynamical behavior near this transition strongly depends on conservation laws. If the system's order parameter is conjugate to a conserved quantity, such as charge, then fluctuations must vanish at the long wavelength limit, i.e. the polarization Π(q=0,Ω ≠0)=0 identically. This is because a conserved quantity such as total charge cannot fluctuate in time. In contrast, when the order parameter is not conserved, there can by strong fluctuations even at long wavelengths, so Π(q=0,Ω) is nonzero.
I will discuss how to calculate the polarization in such situations, focusing on nematic transitions of clean 2D interacting fermions. At the quantum critical point, the dynamical polarization has a nontrivial power-law behavior, Π(q=0,Ω)'' ~ Ω^1/3. I will discuss how this behavior shows up in probes such as polarization resolved Raman scattering. Finally I will compare the theory with some recent measurements on iron based superconductors, most notably FeSe_1-x S_x . Raman experiments on these systems have shown several puzzling features, and our theory resolves some of them nicely.