Semiclassical simulation of quantum spin ice: seeing beyond the light*

We devise a semiclassical numerical method to investigate quantum spin ice, based on classical Monte Carlo and dynamical simulations of the effective ring exchange Hamiltonian in the large-$S$ limit. At low temperatures, this approach is asymptotically equivalent to a path integral field theory, and indeed we find excellent agreement with known results from the latter regarding the dispersion of the photonic modes of the system. We further argue that our method samples the finite-temperature path integral formulation of the quantum spin ice problem accurately, and thus allows us to go beyond the results attainable using the field theoretic description, and study also the isolated as well as collective behaviour of vison excitations.