Semi-classical quantisation of magnetic solitons in the anisotropic Heisenberg quantum chain

TL;DR

This paper applies an algebro-geometric semi-classical quantisation method to the anisotropic Heisenberg quantum chain, linking classical spin wave solutions with quantum eigenstates and analyzing their correlations.

Contribution

It introduces a semi-classical quantisation framework for magnetic solitons in the anisotropic Heisenberg chain using Riemann-Hilbert techniques, connecting classical and quantum descriptions.

Findings

Derived an expression for overlap of semi-classical eigenstates

Linked classical spin waves to quantum eigenstates

Discussed semi-classical correlation functions from phase-space averaging

Abstract

Using the algebro-geometric approach, we study the structure of semi-classical eigenstates in a weakly-anisotropic quantum Heisenberg spin chain. We outline how classical nonlinear spin waves governed by the anisotropic Landau-Lifshitz equation arise as coherent macroscopic low-energy fluctuations of the ferromagnetic ground state. Special emphasis is devoted to the simplest types of solutions, describing precessional motion and elliptic magnetisation waves. The internal magnon structure of classical spin waves is resolved by performing the semi-classical quantisation using the Riemann-Hilbert problem approach. We present an expression for the overlap of two semi-classical eigenstates and discuss how correlation functions at the semi-classical level arise from classical phase-space averaging.