Spin-Ice State of the Quantum Heisenberg Antiferromagnet on the Pyrochlore Lattice

We study the low-temperature physics of the $SU(2)$-symmetric spin-$1/2$ Heisenberg antiferromagnet on a pyrochlore lattice and find fingerprint evidence for the thermal spin-ice state in this frustrated quantum magnet. Our conclusions are based on the results of bold diagrammatic Monte Carlo simulations, with good convergence of the skeleton series down to the temperature $T/J=1/6$. The identification of the spin-ice state is done through a remarkably accurate microscopic correspondence for the static structure factor between the quantum Heisenberg, classical Heisenberg, and Ising models at all accessible temperatures, and the characteristic bowtie pattern with pinch points observed at $T/J=1/6$. The dynamic structure factor at real frequencies (obtained by the analytic continuation of numerical data) is consistent with diffusive spinon dynamics at the pinch points.