A planar diagram approach to the correlation problem

TL;DR

This paper adapts a planar diagram approach from quantum field theory to the Hubbard model of strongly correlated electrons, showing it reduces to solvable diagrams similar to the FLEX approximation, thus expanding solvable models in condensed matter physics.

Contribution

It introduces a planar diagram method for the Hubbard model at large N, connecting quantum field theory techniques to strongly correlated electron systems.

Findings

Hubbard model reduces to planar diagrams at large N.

Generated functional resembles FLEX approximation.

Establishes a new solvable framework for strongly correlated electrons.

Abstract

We transpose an idea of 't Hooft from its context of Yang and Mills' theory of strongly interacting quarks to that of strongly correlated electrons in transition metal oxides and show that a Hubbard model of N interacting electron species reduces, to leading orders in N, to a sum of almost planar diagrams. The resulting generating functional and integral equations are very similar to those of the FLEX approximation of Bickers and Scalapino. This adds the Hubbard model at large N to the list of solvable models of strongly correlated electrons. PACS Numbers: 71.27.+a 71.10.-w 71.10.Fd