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


Exact SO(5) symmetry without fine tuning

Optical traps and lattices provide a new opportunity for studying strongly correlated high-spin physics. We (with J. P. Hu and S. C. Zhang) have made a large progress in spin-3/2 systems (e.g. $^{132}Cs$, ${^9}Be$, $^{135}Ba$, $^{137}Ba$, and $^{201}Hg$) with contact interactions. We proved a generic SO(5) or, isomorphically, Sp(4) symmetry in such systems, which is exact regardless of dimensionality, filling level, and lattice geometry. Various important features from this high symmetr$ studied in the Fermi liquid theory, the mean field phase diagram, and the sign problem in quantum Monte-Carlo simulations. We further explored its consequences and other interesting properties in such systems.

Four-fermion quartetting superfluid

Inspired by the great success of the Feshbach-type experiments, I investigated the four-fermion counterpart of the pairing superfluid in one-dimensional spin-3/2 systems, finding its existence over a large portion in the phase diagram. Moreover, I studied the competition between the pairing and quartetting phases, showing they are Ising dual to each other in one dimension.

Four-site plaquette order

Counter-intuitively, magnetic fluctuations in spin-3/2 systems are even stronger than those with $s = 1/2$ due to the high symmetry. A four-site plaquette order without any site or bond spin orders can be stabilized. We (with S. Chen et al.) constructed an SU(4) Majumdar- Ghosh model, whose solvable ground state exhibits such order in the two-leg ladder systems.

half-quantum vortex

We investigated the HQV in the s-wave quintet Cooper pairing state (S_{pair} = 2) in spin-3/2 systems. The half-quantum vortex loop carries spin quantum numbers as a global analogy to the Cheshire charge in gauge theories. Quantum entanglement is generated during the process of a quasi-particle penetrating the Cheshire-charged HQV loop.

References and talks

  • Congjun Wu, "Hidden symmetry and quantum phases in spin-3/2 cold atomic systems" invited review article, Mod. Phys. Lett. B 20, 1707 (2006), see pdf file.
  • Congjun Wu, "Competing orders in one dimensional spin 3/2 fermionic systems", Phys. Rev. Lett. 95, 266404 (2005), see pdf file.
  • Congjun Wu, Jiangping Hu and Shou-Cheng Zhang, "Quintet pairing and non-Abelian vortex string in spin-3/2 cold atomic systems", cond-mat/0512602.
  • Shu Chen, Congjun Wu, Shou-Cheng Zhang, and Yupeng Wang, "Exact spontaneous plaquette ground states for spin-3/2 ladder models", Phys. Rev. B 72, 214428 (2005) see, pdf file.
  • Congjun Wu, Jiang-ping Hu, and Shou-cheng Zhang, "Exact SO(5) symmetry in the spin 3/2 fermionic system" Phys. Rev. Lett. 91 , 186402(2003), see pdf file .
  • Invited talk at Department of Physics, Ohio State University , Cold Atom Physics Seminar, "Quantum phases of spin-3/2 fermions (PPT) " , May 09, 2006.

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    Last modified: July 15, 2007.