The Memory Function Formalism: A Review

TL;DR

This paper reviews the memory function formalism, a theoretical framework used to analyze optical conductivity in strongly correlated materials, providing detailed mathematical explanations and various approaches for broader understanding.

Contribution

It offers a comprehensive review of the memory function formalism, including mathematical details, different approaches, and applications to dynamical conductivity calculations.

Findings

Provides detailed mathematical derivations

Summarizes approaches like Langevin and projection operator methods

Reviews perturbative expansion and applications to metals

Abstract

An introduction to the Zwanzig-Mori-G\"{o}tze-W\"{o}lfle memory function formalism (or generalized Drude formalism) is presented. This formalism is used extensively in analyzing the experimentally obtained optical conductivity of strongly correlated systems like cuprates and Iron based superconductors etc. For a broader perspective both the generalised Langevin equation approach and the projection operator approach for the memory function formalism are given. The G\"{o}tze-W\"{o}lfle perturbative expansion of memory function is presented and its application to the computation of the dynamical conductivity of metals is also reviewd. This review of the formalism contains all the mathematical details for pedagogical purposes.