Systematic classical continuum limits of integrable spin chains and emerging novel dualities

TL;DR

This paper explores classical continuum limits of integrable quantum spin chains, constructing Lax operators and revealing new dualities between models, enhancing understanding of integrable systems.

Contribution

It introduces a systematic approach to classical continuum limits of various integrable spin chains and uncovers novel dualities linking different models.

Findings

Construction of classical continuum Lax operators for various spin chains

Identification of new dualities between integrable models

Extension to general isotropic and anisotropic gl_n magnets

Abstract

We examine certain classical continuum long wave-length limits of prototype integrable quantum spin chains. We define the corresponding construction of classical continuum Lax operators. Our discussion starts with the XXX chain, the anisotropic Heisenberg model and their generalizations and extends to the generic isotropic and anisotropic gl_n magnets. Certain classical and quantum integrable models emerging from special "dualities" of quantum spin chains, parametrized by c-number matrices, are also presented.