Possible Existence Of Topological Excitations In Quantum Spin Models In Low Dimensions

TL;DR

This paper investigates the presence of topological excitations in low-dimensional quantum spin models, revealing their persistence in certain limits and their connection to well-known topological phenomena.

Contribution

It demonstrates the emergence of topological terms in the partition function of anisotropic quantum Heisenberg models in one and two dimensions using coherent state methods.

Findings

Topological terms contribute to the partition function in ferromagnets.

Topological excitations are retained in the XY limit of 2D ferromagnets.

Results support the quantum Kosterlitz-Thouless scenario.

Abstract

The possibility of existence of topological excitations in the anisotropic quantum Heisenberg model in one and two spatial dimensions is studied using coherent state method. It is found that a part of the Wess-Zumino term contributes to the partition function, as a topological term for ferromagnets in the long wavelength limit in both one and two dimensions. In particular, the XY limit of the two-dimensional anisotropic ferromagnet is shown to retain the topological excitations, as expected from the quantum Kosterlitz-Thouless scenario.