The geometry of antiferromagnetic spin chains

TL;DR

This paper develops a geometric framework for antiferromagnetic spin chains, connecting discrete models to continuum sigma-models with complex flag manifolds as target spaces, using symplectic geometry.

Contribution

It introduces a universal geometric construction of spin chains leading to relativistic sigma-models with arbitrary complex flag manifolds as target spaces.

Findings

Universal expressions for metrics and theta-terms in sigma-models

Construction of spin chains corresponding to complex flag manifolds

Application of symplectic geometry to continuum limit analysis

Abstract

We construct spin chains that describe relativistic sigma-models in the continuum limit, using symplectic geometry as a main tool. The target space can be an arbitrary complex flag manifold, and we find universal expressions for the metric and theta-term.