First-order phase transitions in the square-lattice easy-plane J-Q model

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 discontinuous transition on the largest lattices 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 rather small lattices of size L≈16. A parameter 0≤λ≤1 [λ=0 being the easy-plane model and λ=1 being the SU(2) symmetric J-Q model] allows us to smoothly interpolate between these two limiting models. We use stochastic series expansion (SSE) quantum Monte Carlo (QMC) to investigate the nature of this transition as λ is varied - here we present studies for λ=0,0.5,0.75,0.85,0.95, and 1. While we find that the first-order transition weakens as λ is increased from 0 to 1, we find no evidence that the transition becomes continuous until the SU(2) symmetric point, λ=1. We thus conclude that the square-lattice superfluid-VBS transition in the two-component easy-plane model is generically first order.