Transport in a long-range classical field theory

In recent years, integrable spin chains have been demon-

strated to have anomalous transport characterized by Kardar-Parisi-

Zhang (KPZ) scaling in non-equilibrium correlations. Such spin mod-

els, whether quantum or classical, often feature local interactions with

a non-Abelian symmetry. In this work, we investigate a long-range in-

tegrable spin chain known as the half-wave map model at finite tem-

perature, which is the classical continuum limit of the Haldane-Shastry

model with inverse-square interactions. At thermal equilibrium, we ob-

serve asymptotic freedom reminiscent of the two-dimensional non-linear

sigma model. In out-of-equilibrium quenches, the model reveals distinc-

tive features of the underlying integrability and Yangian symmetry. We

also attempt to quantify the crossover to a classical Heisenberg chain

through an intermediate Inozemtsev-like model.