Optical sum rules that relate to the potential energy of strongly correlated systems

TL;DR

This paper develops sum rules for inelastic light scattering that connect the first moment of the response to the potential energy in strongly correlated systems, offering insights into electronic excitations across the Brillouin zone.

Contribution

It introduces new sum rules linking light scattering response to potential energy and details their polarization dependence in strongly correlated materials.

Findings

Sum rules relate response moments to potential energy.

Polarization dependence reveals electronic excitations in different Brillouin zone regions.

Comparison with experiments on SmB_6 supports the theoretical results.

Abstract

A class of sum rules for inelastic light scattering is developed. We show that the first moment of the non-resonant response provides information about the potential energy in strongly correlated systems. The polarization dependence of the sum rules provide information about the electronic excitations in different regions of the Brillouin zone. We determine the sum rule for the Falicov-Kimball model, which possesses a metal-insulator transition, and compare our results to the light scattering experiments in SmB_6.