t-J model then and now: A personal perspective from the pioneering times

TL;DR

This paper reviews the historical development and core concepts of the t-J model in strongly correlated magnetic metals, emphasizing its evolution, generalizations, and the introduction of real space and hybrid pairing ideas.

Contribution

It provides a personal historical perspective on the t-J model's development, clarifies its original meaning, and discusses recent generalizations and new pairing concepts.

Findings

The t-J model was first derived 30 years ago as a key framework for strongly correlated metals.

Introduction of real space pairing concept in the context of the t-J model.

Proposal of hybrid pairing as a new concept in the model's framework.

Abstract

In this overview I sketch briefly the path to the so-called {\em t-J model} derived for the first time 30 years ago and provide its original meaning within the theory of strongly correlated magnetic metals with a non-Fermi (non-Landau) liquid ground state. An emergence of the concept of {\em real space pairing}, is discussed in a historical prospective. A generalization of this model to the many-orbital situation is briefly discussed. The emphasis is put on didactical exposition of ideas, as they were transformed into mathematical language. The concept of {\em hybrid pairing} is introduced in the same context at the end.