Integrable quantum spin chains and their classical continuous counterparts

TL;DR

This paper explores the classical continuum limits of integrable quantum spin chains, deriving corresponding Lax operators and illustrating with the isotropic and anisotropic Heisenberg models.

Contribution

It introduces a method to obtain classical continuum Lax operators from quantum spin chains and applies it to specific models.

Findings

Derived classical continuum Lax operators for quantum spin chains

Established continuum limits for Heisenberg models

Provided explicit examples of classical counterparts

Abstract

We present certain classical continuum long wave-length limits of prototype integrable quantum spin chains, and define the corresponding construction of classical continuum Lax operators. We also provide two specific examples, i.e. the isotropic and anisotropic Heisenberg models.