Spin wave analysis of Heisenberg magnets in restricted geometries

TL;DR

This paper reviews the spin wave theory applied to low-dimensional Heisenberg magnets, focusing on a two-leg ferrimagnetic ladder, and compares theoretical results with numerical estimates.

Contribution

It introduces the spin-wave technique using Dyson--Maleev bosons for a specific model and discusses recent modifications for disordered phases.

Findings

Spin wave theory provides accurate zero-temperature results for low-dimensional Heisenberg systems.

The Dyson--Maleev formalism is effective up to second order in interactions.

Theoretical results align well with numerical estimates.

Abstract

In the last decade it has been proven that the standard spin wave theory was able to provide accurate zero-temperature results for a number of low-dimensional Heisenberg spin systems. In this chapter we introduce the main ingredients of the spin-wave technique using as a working model the two-leg mixed-spin ferrimagnetic ladder and the Dyson--Maleev boson formalism up to second order in the spin-wave interaction. In the remainder, we survey typical applications in low-space dimensionality as well as some recent modifications of the theory admitting a quantitative analysis in magnetically disordered phases. The presented spin-wave results are compared with available numerical estimates.