Principal Chiral Model in Correlated Electron 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 $\mathrm{Tr}\left({\partial }_{a}U{\partial }_a{U}^{†}\right)$ 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 $\text{SO}(3)\times \text{SO}(3)\to \text{SO}(3)$.

arXiv comment5 pages, 2 figures

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Cited by in corpus (7)

• New Soft Theorems for Goldstone Boson Amplitudes
• A solvable 3D Kondo lattice exhibiting odd-frequency pairing and order fractionalization
• Skyrmions and Hopfions in 3D Frustrated Magnets
• Improvement of a conserved current density versus adding a total derivative to a Lagrangian density
• Interpolating Between $CP(N-1)$ and $S^{2N-1}$ Target Spaces
• Sigma model on a squashed sphere with a Wess-Zumino term
• Remarks on Baby Skyrmion Lie-Algebraic Generalization