Spherically symmetric approaches in the theoretical study of low-dimensional magnets

TL;DR

This paper reviews spherically symmetric self-consistent methods for analyzing low-dimensional magnetic systems, addressing traditional analysis difficulties and extending to complex models like Hubbard and Kondo lattice.

Contribution

It introduces and discusses the application of spherically symmetric approaches to a wide range of low-dimensional spin models, including frustrated and complex systems.

Findings

Methods respect the Mermin-Wagner and Marshall theorems.

Approach avoids traditional analysis difficulties in low-dimensional magnets.

Applicable to complex models like Hubbard, t-J, and Kondo lattice.

Abstract

The main ideas and some of the most important results of the spherically symmetric self-consistent approach and a number of related theoretical algorithms are presented. These methods make it possible to study low-dimensional Heisenberg-type spin models, including frustrated ones, with careful consideration of the theoretic (Mermin-Wagner and Marshall) theorems, as well as the site spin constraint. Thus, the difficulties that may arise in the traditional analysis of low-dimensional magnetic systems are avoided. The approach can also be applied to the spin-pseudospin model, and is also embedded in more complex constructions when considering spin models with free carriers, such as the basic and three-band Hubbard models, t-J and s-d models, and the Kondo lattice.