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

2010/05/31 by Jean Avan, Anastasia Doikou, Konstadinos Sfetsos · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Anisotropy #Antiferromagnetism #Black Holes and Theoretical Physics #Chain (unit) #Classical limit #Heisenberg model #Integrable system #Isotropy #Mathematical physics #Nonlinear Waves and Solitons #Physics #Quantum #Quantum mechanics #Spin (aerodynamics) #Theoretical physics #cond-mat.stat-mech #hep-th #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1016/j.nuclphysb.2010.07.014

published as Nucl.Phys.B840:469-490,2010 · 29 pages, Latex. Two references added, a few typos corrected, version to appear in NPB

openalex publication_date 2010/08/04 · arxiv created 2010/08/05 · arxiv updated 2014/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Quantum inverse problem method. I
• The generalized non-linear Schrödinger model on the interval
• Boundary conditions for integrable quantum systems

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