Principal Chiral Model in Correlated Electron Systems

TL;DR

This paper explores noncollinear magnetic phenomena in correlated electron systems, modeling their low-energy behavior with a class of sigma models that interpolate between classical Heisenberg and principal chiral models, revealing complex symmetry structures.

Contribution

It introduces a unified sigma model framework for noncollinear magnetic orders on 2D and 3D lattices, generalizing to symmetry-breaking cases and connecting to principal chiral models.

Findings

Low-energy theories described by a one-parametric sigma model.

Interconnection between Heisenberg and principal chiral models.

Extension to symmetry-breaking in 3D systems.

Abstract

We discuss noncollinear magnetic phenomena whose local order parameter is characterized by more than one spin vector. By focusing on the simple cases of 2D triangular and 3D pyrochlore lattices, we demonstrate that their low-energy theories can be described by a one-parametric class of sigma models continuously interpolating between the classical Heisenberg model and the principal chiral model ${\rm Tr} \,\left( \partial_a U \partial_a U^\dagger\right)$ for all $U\in \text{SU}(2)$. The target space can be viewed as a U$(1)$ fibration over the $CP(1)$ space. The 3D version of our model is further generalized to break spatial and spin rotation symmetry $\text{SO}(3) \times \text{SO}(3) \to \text{SO}(3)$.