B-1g Raman scattering through a quantum critical point

A wide variety of strongly correlated insulators ranging from intermediate valence materials, to Kondo insulators, to underdoped high-temperature supe rconductors display anomalous behavior in their inelastic light scattering. The Raman response in these materials shows a low-temperature transfer of spectral weight from low to high energy (as T is reduced), the appearance o f an isosbestic point (a characteristic frequency where the Raman response is independent of temperature), and a large ratio of twice the "spectral ga p" to the "onset temperature" where the low-energy spectral weight begins t o deplete. We illustrate how these features generically appear in the Raman response of model systems that are tuned to lie just on the insulating sid e of the metal-insulator transition. We solve for the Raman response in the Falicov-Kimball model and in the Hubbard model. In the latter case, we fin d a number of new features arise as one approaches the metal-insulator tran sition from the metallic Fermi-liquid phase. Such behavior has not yet been seen in experiment.