Principal Chiral Model in Correlated Electron Systems

Understand

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 $\text{SO}(3) \times \text{SO}(3) \to \text{SO}(3)$.