Exact Optical Dielectric Function of a Nearly Homogeneous Solid

TL;DR

This paper derives an exact expression for the optical dielectric function of a nearly homogeneous solid using a solvable model, applicable at zero temperature across various dimensions, and argues its relevance to real materials.

Contribution

It provides the first exact calculation of the optical dielectric function for a nearly homogeneous solid within an exactly solvable model, extending the understanding of dielectric properties in such systems.

Findings

Exact dielectric function derived for the model

Applicable in any number of spatial dimensions

Relevant to real nearly homogeneous solids in RPA limit

Abstract

Based on an exactly solvable model of a nearly homogeneous solid (jellium+phonons), we compute the optical dielectric function exactly at zero temperature in any number of spatial dimensions. It is argued as we have done elsewhere, that the answer for the optical dielectric function we obtain is in fact the exact answer for a real nearly homogeneous solid in the same limit in which RPA itself is exact.