Are antiferromagnetic spin chains representations of the higher Wess-Zumino-Witten models?

Abstract

We show that while the exactly integrable spin-(3/2 Heisenberg antiferromagnet is a representation of the nonlinear \ensuremath{\sigma} model with nontrivial Wess-Zumino term, the generic massless antiferromagnet has long-wavelength behavior equivalent to spin (1/2. This is demonstrated by comparing the predictions of conformal symmetry and rotational symmetry to the gaps calculated for finite chains. The leading corrections are eliminated leading to stable estimates of the conformal central charge and exponents for the spin-correlation functions.