  Ice states, in which frustrated interactions lead to a macroscopic
ground-state degeneracy, occur in water ice, in problems of frustrated charge
order on the pyrochlore lattice, and in the family of rare-earth magnets
collectively known as spin ice. Of particular interest at the moment are
"quantum spin ice" materials, where large quantum fluctuations may permit
tunnelling between a macroscopic number of different classical ground states.
Here we use zero-temperature quantum Monte Carlo simulations to show how such
tunnelling can lift the degeneracy of a spin or charge ice, stabilising a
unique "quantum ice" ground state --- a quantum liquid with excitations
described by the Maxwell action of 3+1-dimensional quantum electrodynamics. We
further identify a competing ordered "squiggle" state, and show how both
squiggle and quantum ice states might be distinguished in neutron scattering
experiments on a spin ice material.
