Quantum Ice: A Quantum Monte Carlo Study

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, stabilizing 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.