Quadrupolar Order in Quantum Spin Ice

Quantum effects in spin ice can modelled using an XXZ model on the pyrochlore lattice. For unfrustrated interactions, $J_\pm > 0$, this model is accessible to quantum Monte Carlo simulations, and supports a quantum spin liquid ground state for $0 < J_\pm \sim < 0.05 J_{zz}$. Here we present a study of this model for frustrated interactions, $J_\pm < 0$, using a combination of classical Monte Carlo and semi-classical molecular-dynamics simulations. We find that, for $J_\pm < -0.5 J_{zz}$, the spin liquid gives way with a phase with hidden quadrupolar order.