Abstract
We study the classical and quantum phase transitions of Sp(4) spin systems on three-dimensional stacked square and triangular lattices. We present general Ginzburg-Landau field theories for various types of Sp(4) spin orders with different ground-state manifolds such as CP(3), ${S}^{7}/{Z}_{2}$, Grassmann manifold ${G}_{2,5}$, ${G}_{2,6}$, and so on, based on which the nature of the classical phase transitions are studied, and a global phase diagram is presented. The classical phase transitions close to quantum phase transitions toward spin-liquid states are also discussed based on renormalization group flow. Our results can be directly applied to the simplest Sp(4) and SU(4) Heisenberg models which can be realized using spin-3/2 atoms and alkaline-earth atoms trapped in optical lattice.
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