The Zubarev Double Time Greens function-A Vintage Many Body Technique

TL;DR

This paper introduces the Zubarev Double Time Greens Function technique, a powerful many-body physics method from the 1960s, demonstrating its applications to electron gases, the Hubbard model, and phenomena like ferromagnetism and superconductivity.

Contribution

It provides a comprehensive, pedagogical presentation of the Zubarev Double Time Greens Function method and illustrates its applications to key many-body problems.

Findings

Application to non-interacting electron and boson gases

Derivation of the Stoner criterion for ferromagnetism from the Hubbard model

Extension potential to superconductivity and related phenomena

Abstract

These lecture notes present a comprehensive and powerful many-body technique pioneered in 1960 by D. N. Zubarev. The technique, known as the Zubarev Double Time Greens Function method, was used extensively by leading solid state physicists such as John Hubbard and Laura Roth in the 1960s. We present the technique and apply it to the non-interacting electron and boson gas. We next consider the (many-body) Hubbard model and show how it yields the Stoner criterion for ferromagnetism. It is easily extendable to superconductivity and related problems. Our treatment is pedagogical and understandable to those with just an elementary understanding of second quantization.