  Presented is an unitary operator splitting method for handling the
spin-density interaction in spinor Bose-Einstein condensates. The zero
temperature behavior of a spinor BEC is given by mean field theory, where the
Hamiltonian includes a nonlinear hyperfine spin interaction. This hyperfine
interaction has a diagonal probability-density term (leading to the usual
Gross-Pitaevskii type equation of motion) but also has a nondiagonal
spin-density term. Since the F=2 spinor BEC (spin-2 BEC) has a non-Abelian
superfluid phase (nonperturbative cyclic phase in the strong spin-density
coupling regime), an infinite-order expansion of the quantum evolution operator
is 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.
