We study the quantum phase transition between the superfluid and valence bond solid in "easy-plane" J-Q models on the square lattice. The Hamiltonian we study is a linear combination of two model Hamiltonians: (1) an SU(2) symmetric model, which is the well known J-Q model that does not show any direct signs of a discontinious transition even on lattices as large as $512\times 512$ and is presumed continuous, and (2) an easy plane version of the J-Q model, which shows clear evidence for a first order transition even on $L\approx16$... (read more)

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