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The peculiar features of quantum magnetism sometimes forbid the existence ofgapped `featureless' paramagnets which are fully symmetric andunfractionalized. The Lieb-Schultz-Mattis theorem is an example of such aconstraint, but it is not known what the most general restriction might be. Wefocus on the existence of featureless paramagnets on the spin-1 square latticeand the spin-1 and spin-1/2 honeycomb lattice with spin rotation and spacegroup symmetries in 2+1D. Although featureless paramagnet phases are not ruledout by any existing theorem, field theoretic arguments disfavor theirexistence. Nevertheless, by generalizing the construction of Affleck, Kennedy,Lieb and Tasaki to a class we call `slave-spin' states, we propose featurelesswave functions for these models. The featureless-ness of the spin-1 slave-spinstates on the square and honeycomb lattice are verified both analytically andnumerically, but the status of the spin-1/2 honeycomb state remains unclear.

The Existence of Featureless Paramagnets on the Square and the Honeycomb Lattices in 2+1D