<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi mathvariant="normal">SU</mml:mi><mml:mo>(</mml:mo><mml:mi>N</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math> symmetry with ultracold alkali dimers: Weak dependence of scatteri

We investigate the prospect of using ultracold alkali diatomic molecules to implement many-body quantum systems with <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi mathvariant="normal">SU</a:mi><a:mo>(</a:mo><a:mi>N</a:mi><a:mo>)</a:mo></a:mrow></a:math> symmetry. Experimentally accessible molecules offer large <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>N</c:mi></c:math> for both bosonic and fermionic systems, with both attractive and repulsive interactions. We carry out coupled-channel scattering calculations on pairs of NaK, NaRb, and NaCs molecules that are shielded from destructive collisions with static electric fields. We develop new methods to handle the very large basis sets required to include nuclear spins. We show that all the molecules studied have the properties required for <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mi mathvariant="normal">SU</d:mi><d:mo>(</d:mo><d:mi>N</d:mi><d:mo>)</d:mo></d:mrow></d:math> symmetry: the collisions are principally elastic, and the scattering lengths depend only weakly on the spin states of the molecules. The rates of spin-changing inelastic collisions are very low. We develop and test a semiclassical model of the spin dependence and find that it performs well.