Exact theory for electronic Raman scattering of correlated materials in infinite dimensions

A wide variety of strongly correlated materials including ${\mathrm{SmB}}_{6},$ FeSi, and the underdoped cuprates display anomalous behavior in their Raman response, which includes a low-temperature transfer of spectral weight from low to high energy (as T is reduced) and the appearance of an isosbestic point (a characteristic frequency where the Raman response is independent of temperature). We illustrate how these features appear in the Raman response of the infinite-dimensional Hubbard model, which is the simplest system to undergo the Mott transition from a Fermi liquid phase. We find that the qualitative behavior in the insulating phase is model independent, and that a number of new features arise as one approaches the metal-insulator transition from the Fermi-liquid phase. Such behavior has not yet been seen in experiment. We propose a number of different systems that are likely to show these new anomalies.