On the Discrete and Continuum Integrable Heisenberg Spin Chain Models

拓也 小林

N. Papanicolaou

Haldane (1982) conjectured that a simple generalisation of the Heisenberg spin chain leads to a completely integrable classical system without invoking the usual continuum approximation. Complete integrability is established for the generalised discrete chain by exhibiting a Lax pair and an infinite set of non-local conservation laws. The associated inverse scattering problem is also formulated providing explicit soliton solutions.

A. Kundu, B. Basu-Mallick

Robin Steinigeweg, Heinz–Jürgen Schmidt

F. D. M. Haldane

A rotationally invariant translation-generating functional for the continuum model of a ferromagnetic chain is found, resolving a long-standing paradox. The condition of rotational invariance leads to a topological quantization in the continuum classical model that corresponds to spin quantization in the equivalent discrete quantum model. The relation between the classical continuum model and the discrete quantum models is made precise.

Jean Avan, Anastasia Doikou, Konstadinos Sfetsos

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.