Hidden symmetry and quantum phases in spin-3/2 cold atomic systems

TL;DR

This paper reviews the hidden symmetries and quantum phases in spin-3/2 cold atomic systems, highlighting their unique properties, phases, and the effects of quantum fluctuations, with implications for high spin quantum simulations.

Contribution

It demonstrates the presence of generic SO(5) symmetry in spin-3/2 systems and explores its implications for various quantum phases and phenomena.

Findings

Identification of SO(5) symmetry in high spin fermionic systems

Discovery of non-Abelian properties in half-quantum vortices

Quantum fluctuations are stronger in spin-3/2 than in spin-1/2 systems

Abstract

Optical traps and lattices provide a new opportunity to study strongly correlated high spin systems with cold atoms. In this article, we review the recent progress on the hidden symmetry properties in the simplest high spin fermionic systems with hyperfine spin $F=3/2$, which may be realized with atoms of $^{132}$Cs, $^9$Be, $^{135}$Ba, $^{137}$Ba, and $^{201}$Hg. A {\it generic} SO(5) or isomorphically, $Sp(4)$) symmetry is proved in such systems with the s-wave scattering interactions in optical traps, or with the on-site Hubbard interactions in optical lattices. Various important features from this high symmetry are studied in the Fermi liquid theory, the mean field phase diagram, and the sign problem in quantum Monte-Carlo simulations. In the s-wave quintet Cooper pairing phase, the half-quantum vortex exhibits the global analogue of the Alice string and non-Abelian Cheshire charge properties in gauge theories. The existence of the quartetting phase, a four-fermion counterpart of the Cooper pairing phase, and its competition with other orders are studied in one dimensional spin-3/2 systems. We also show that counter-intuitively quantum fluctuations in spin-3/2 magnetic systems are even stronger than those in spin-1/2 systems.