Optical Sum Rule in Strongly Correlated Systems

TL;DR

This paper investigates the optical sum rule in strongly correlated systems, demonstrating that while the fundamental sum rule holds, the optical integral varies with parameters, potentially explaining experimental observations of apparent violations.

Contribution

The study applies the DMFT+Sigma approach to two models, showing the sum rule's validity and how the optical integral's dependence on parameters can mimic violations.

Findings

The Kubo sum rule is satisfied in both models.

Optical integral depends on temperature and parameters, leading to apparent violations.

Results align with experimental observations of optical sum rule deviations.

Abstract

We discuss the problem of a possible "violation" of the optical sum rule in the normal (non superconducting) state of strongly correlated electronic systems, using our recently proposed DMFT+Sigma approach, applied to two typical models: the "hot - spot" model of the pseudogap state and disordered Anderson - Hubbard model. We explicitly demonstrate that the general Kubo single band sum rule is satisfied for both models. However, the optical integral itself is in general dependent on temperature and characteristic parameters, such as pseudogap width, correlation strength and disorder scattering, leading to effective "violation" of the optical sum rule, which may be observed in the experiments.