A Large-$S$ Study of Quantum Kagome Ice

We present a large-$S$ study of a quantum spin ice Hamiltonian, introduced by Huang, et al., [PRL 112, 167203 (2014)], on the kagome lattice. This model involves a competition between the frustrating Ising term of classical kagome ice, a Zeeman magnetic field $h$,and a nearest-neighbor transverse spin-flip term $S_i^x{S}_j^x-S_i^y{S}_j^y$. Recent Quantum Monte Carlo (QMC) simulations by Carrasquilla, et al., [Nature Communications, 6, 7421, (2015)], uncovered lobes of a disordered phase for large Ising interaction and $h\mathrm{\ne }0$ – a putative quantum spin liquid phase. Here, we examine the nature of this model using large-$S$ expansion. We show that the ground state properties generally have the same trends with those observed in QMC simulations. In particular, the large-$S$ ground state phase diagram captures the existence of the disordered lobes.