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Presented is an unitary operator splitting method for handling thespin-density interaction in spinor Bose-Einstein condensates. The zerotemperature behavior of a spinor BEC is given by mean field theory, where theHamiltonian includes a nonlinear hyperfine spin interaction. This hyperfineinteraction has a diagonal probability-density term (leading to the usualGross-Pitaevskii type equation of motion) but also has a nondiagonalspin-density term. Since the F=2 spinor BEC (spin-2 BEC) has a non-Abeliansuperfluid phase (nonperturbative cyclic phase in the strong spin-densitycoupling regime), an infinite-order expansion of the quantum evolution operatoris needed for quantum simulation applications. An infinite-order expansion,obtained by analytical continuation and expressed in analytically closed form,for the spin-2 BEC is presented.

Quantum lattice gas model of spin-2 Bose-Einstein condensates and  closed-form analytical continuation of nonlinear interactions in spin-2  superfluids