Topological term in the non-linear $\sigma$ model of the SO(5) spin chains

Abstract

We show that there is a topological (Berry phase) term in the non-linear $\sigma$ model description of the SO(5) spin chain. It distinguishes the linear and projective representations of the SO(5) symmetry group, in exact analogy to the well-known $\theta$-term of the SO(3) spin chain. The presence of the topological term is due to the fact that ${\pi }_2(\frac{SO(5)}{SO(3)\times SO(2)})=\mathbb{Z}$. We discuss the implication of our results on the spectra of the SO(5) spin chain, and connect it with a recent solvable SO(5) spin model which exhibits valence bond solid ground state and edge degeneracy.

12 pages, 1 figure; the publication version

References in corpus (4)

• Competing orders in one dimensional spin 3/2 fermionic systems
• Hidden symmetry and quantum phases in spin-3/2 cold atomic systems
• Class of exactly solvable SO(n) symmetric spin chains with matrix product ground states
• Spin-quadrupole ordering of spin-3/2 ultracold fermionic atoms in optical lattices in the one-band Hubbard model

Cited by in corpus (2)

• Quantum magnetism of ultra-cold fermion systems with the symplectic symmetry
• Topological interactions of Nambu-Goldstone bosons in quantum many-body systems