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

TL;DR

This paper models quantum monopole motion in spin ice as a quantum percolation problem, revealing fractal wavefunctions and diffusive behavior influenced by spin configurations and disorder, aligning with experimental findings.

Contribution

It introduces a theory linking quantum monopole diffusion in spin ice to quantum percolation, highlighting fractal wavefunctions and the impact of spin configuration bimodality.

Findings

Monopole motion reduces to quantum diffusion due to blocked directions.

Monopole wavefunctions exhibit fractal, non-ergodic characteristics.

Spectral functions align with experimental observations.

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. The hopping amplitude of a monopole is sensitive to the configuration of its surrounding spins, taken to be quasi-static on the relevant timescales. This leads to well-known blocked directions in the monopole motion; we find that these are 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 $\approx 1/3$ 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 wavefunctions appear to be fractal; we explain this observation via a mapping to quantum percolation on trees. The fractal, non-ergodic nature of monopole wavefunctions manifests itself in the low-frequency behavior of monopole spectral functions, and is consistent with experimental observations.