Quantum percolation of monopole paths and the response of quantum spin ice

We consider quantum spin ice in a temperature regime in which its response is dominated by the coherent motion of a dilute gas of monopoles through an incoherent spin background, taken to be quasistatic on the relevant timescales. The latter introduces well-known blocked directions that we find sufficient to reduce the coherent propagation of monopoles to quantum diffusion. This result is robust against disorder, as a direct consequence of the ground-state degeneracy, which disrupts the quantum interference processes needed for weak localization. Moreover, recent work [Tomasello et al., Phys. Rev. Lett. 123. 067204 (2019)] has shown that the monopole hopping amplitudes are roughly bimodal: for approximate to 1/3 of the flippable spins surrounding a monopole, these amplitudes are extremely small. 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 wave functions appear to be fractal; we explain this observation via mapping to quantum percolation on trees. The fractal, nonergodic nature of monopole wave functions manifests itself in the low-frequency behavior of monopole spectral functions, and is consistent with experimental observations.

Automated summary

This study investigates the response of quantum spin ice in a specific temperature range, finding that the propagation of monopoles can be transformed into quantum diffusion, with the results being robust and consistent with experimental observations.