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arXiv:cond-mat/0608690 · Modern Physics Letters B

HIDDEN SYMMETRY AND QUANTUM PHASES IN SPIN-3/2 COLD ATOMIC SYSTEMS

Congjun Wu

Published Nov 30, 2006• 176 citations
arXivHTMLPDF

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 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.

DOI
10.1142/s0217984906012213

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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 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.
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We study various Mott insulating phases of interacting spin-32\frac{3}{2}23​ fermionic ultracold atoms in two-dimensional square optical lattices at half filling. Using a generalized one-band Hubbard model with hidden SO(5) symmetry, we identify two distinct symmetry breaking phases: the degenerate antiferromagnetic spin-dipole--spin-octupole ordering and spin-quadrupole ordering, depending on the sign of the spin-dependent interaction. These two competing orders exhibit very different symmetry properties, low energy excitations, and topological characterizations. Near the SU(4) symmetric point, a quantum critical state with a $\ensuremath{\pi}$-flux phase may emerge due to strong quantum fluctuations, leading to spin algebraic correlations and gapless excitations.