Self-consistency functional equation in strongly correlated electron systems: a different approach

TL;DR

This paper introduces a novel differential equation approach to the self-consistency functional equation in strongly correlated electron systems, enabling analysis in the small exchange energy limit and comparison with numerical results.

Contribution

A new differential equation method for the self-consistency functional equation in strongly correlated systems, especially effective as exchange energy approaches zero.

Findings

Solutions agree with existing numerical calculations

Method effectively studies the J→0 limit

Applicable to various strongly correlated electron systems

Abstract

We propose a new approach to the self-consistency equation, which arises in the problem of the motion of a hole in a quantum antiferromagnet, appropriate to the case of small exchange energy $J$. The functional equation for the Green function is transformed into a differential equation; its solutions are analyzed and compared to the existing numerical calculations. This method allows one to study the limit of $J\to 0$. Application to other strongly correlated electron systems is discussed.