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

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Moessner,  Roderich
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Stern, M., Castelnovo, C., Moessner, R., Oganesyan, V., & Gopalakrishnan, S. (2021). Quantum percolation of monopole paths and the response of quantum spin ice. Physical Review B, 104(11): 115114. doi:10.1103/PhysRevB.104.115114.


Cite as: https://hdl.handle.net/21.11116/0000-0009-5A0E-4
Abstract
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.