Quantum percolation of monopoles and the response of quantum spin ice

The low temperature (magnetic) response of quantum spin ice is dominated by the coherent motion of a dilute gas of monopoles. Contrary to conventional modelling that assumes a uniform distribution of hopping amplitudes for such dynamics, recent work by Tommasello et al. has demonstrated that the distribution is in fact bimodal, and strongly correlated with the surrounding spin configuration. The larger of the two amplitudes occurs on average 2/3 of the times, and is responsible for the coherent motion of monopoles. The smaller one, on the other hand, induces dynamics that is far slower than the expected decoherence time scales in a solid state system. We exploit this structure to construct a theory of quantum monopole motion in spin ice in the limit where the slow hopping terms are set to zero. The monopole wavefunctions are fractal. The non-ergodic nature of monopole motion manifests itself in the low-frequency behaviour of spin response, and is consistent with experimental observations. We further extend our results to the case of disordered spin ice.