SU(n) and Quantum SU(n) Symmetries in Physical Systems

T. Zavertanyi, Alexei K. Kolezhuk

We study antiferromagnetic systems with enhanced “nearly-SU(N)” symmetry, which can be realized in systems of ultracold spinor atoms in optical lattices. Examples of N = 3 (for S = 1 bosons) and N = 4 (for S=32 fermions) are considered. Near the SU(N) point, the low-energy physics can be described by the CPN−1 model with an additional symmetry-breaking term lowering the symmetry down to SU(2) and favoring the Néel ordering. We show that the effective theory of such systems can be cast in the form of a nonlinear sigma model with the SO(3) matrix-valued field, which is typically obtained for frustrated magnets with non-collinear order. Further, we show that those systems possess a peculiar effect of topological binding: for a system with the underlying spin S, lowering of the symmetry from SU(2S + 1) to SU(2) leads to binding of topological unit-charge excitations of the CP2S model (skyrmions for space dimension d = 2, instantons for d = 1, and hedgehogs for d = 3) into 2S-multiplets.

Michel Le Bellac

Weixin Liu, Xiaotong Lu, Ting Li +4 more

Simulating physics with large $\mathrm{SU}(N)$ symmetry is one of the unique advantages of alkaline-earth-metal atoms. Introducing periodical driving modes to the system may provide richer $\mathrm{SU}(N)$ physics that the static one cannot reach. However, a discussion of whether or not the driving modes will break the SU($N$) symmetry is still lacking. Here we experimentally study a Floquet engineered degenerate $^{87}\mathrm{Sr}$ optical lattice clock (OLC) by periodically modulating the frequency of the lattice laser. With the help of Rabi spectroscopy, we find that the atoms at different Zeeman sublevels are tuned by the same driven function. Meanwhile, our experimental results suggest that the uniform distribution among the sublevels does not change despite the driving. Our experimental demonstrations may pave the way for implementation of Floquet engineering on tailoring the $\mathrm{SU}(N)$ physics in the OLC system.

H. Y. Cui

We show that the relativistic matter waves of two particle system contains the SU(2) symmetry; the relativistic matter waves of three particle system contains the SU(3) symmetry. Therefore, the relativistic matter wave is suitable for describing many-particle system such as quarks or gluons etc that are engaged with implicated symmetry problems. The weak interaction and strong interaction are investigated by using the relativistic de Broglie matter wave with SU(n) symmetry. Our results agree well with experiments. This work is to re-discover and re-explore de Broglie matter wave with the SU(n) symmetry and its applications to particle physics. This work was divided into two parts: Chapter 1, Relativistic de Broglie matter wave; Chapter 2, Factory of prosthesis.