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Motivated by recent observations (P. Soltan-Panahi {\it et al.}, NaturePhysics {\bf 8}, 71-75 (2012)), we study the stability of a Bose-EinsteinCondensate within a spin-dependent honeycomb lattice towards forming a "TwistedSuperfluid" state. Our exhaustive numerical search fails to find this phase,pointing to possible non-mean field physics.

Absence of the Twisted Superfluid State in a mean field model of bosons on a Honeycomb Lattice