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Corfu Summer Institute School and Workshops on Elementary Particle Physics and Gravity (CORFU)

Integrable quantum spin chains and their classical continuous counterparts

Anastasia Doikou, Jean Avan, Konstadinos Sfetsos

Published Apr 1, 2011• 0 citations
Publisher

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.
DOI
10.22323/1.127.0016

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The integrability aspects of a classical one-dimensional continuum isotropic biquadratic Heisenberg spin chain in its continuum limit up to order [O(a4)] in the lattice parameter ‘‘a’’ are studied. Through a differential geometric approach, the dynamical equation for the spin chain is expressed in the form of a higher-order generalized nonlinear Schrödinger equation (GNLSE). An integrable biquadratic chain that is a deformation of the lower-order continuum isotropic spin chain, is identified by carrying out a Painlevé singularity structure analysis on the GNLSE (also through gauge analysis) and its properties are discussed briefly. For the nonintegrable chain, the perturbed soliton solution is obtained through a multiple scale analysis.