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# Experimental signatures of emergent quantum electrodynamics in Pr2Hf2O7

## Abstract

In a quantum spin liquid, the magnetic moments of the constituent electron spins evade classical long-range order to form an exotic state that is quantum entangled and coherent over macroscopic length scales1,2. Such phases offer promising perspectives for device applications in quantum information technologies, and their study can reveal new physics in quantum matter. Quantum spin ice is an appealing proposal of one such state, in which the fundamental ground state properties and excitations are described by an emergent U(1) lattice gauge theory3,4,5,6,7. This quantum-coherent regime has quasiparticles that are predicted to behave like magnetic and electric monopoles, along with a gauge boson playing the role of an artificial photon. However, this emergent lattice quantum electrodynamics has proved elusive in experiments. Here we report neutron scattering measurements of the rare-earth pyrochlore magnet Pr2Hf2O7 that provide evidence for a quantum spin ice ground state. We find a quasi-elastic structure factor with pinch points—a signature of a classical spin ice—that are partially suppressed, as expected in the quantum-coherent regime of the lattice field theory at finite temperature. Our result allows an estimate for the speed of light associated with magnetic photon excitations. We also reveal a continuum of inelastic spin excitations, which resemble predictions for the fractionalized, topological excitations of a quantum spin ice. Taken together, these two signatures suggest that the low-energy physics of Pr2Hf2O7 can be described by emergent quantum electrodynamics. If confirmed, the observation of a quantum spin ice ground state would constitute a concrete example of a three-dimensional quantum spin liquid—a topical state of matter that has so far mostly been explored in lower dimensionalities.

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## Acknowledgements

We acknowledge the Institut Laue-Langevin (Grenoble, France) for the allocated beamtime. We acknowledge funding from the Swiss National Science Foundation (grant nos 200021_140862; 206021_139082; and 200021_138018). This research used resources at the Spallation Neutron Source, a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory. The work at ORNL was supported by the US DOE, Office of Science, Office of Basic Energy Sciences, under contract number DE-AC05-00OR22725. The work at the University of Warwick was supported by the EPSRC, UK, through grant EP/M028771/1. Additional neutron scattering experiments were carried out at the continuous spallation neutron source SINQ at the Paul Scherrer Institut at Villigen PSI in Switzerland.

## Author information

Project and experiments were designed by R.S., T.F. and M.K. Crystal growth and characterization were performed by R.S., M.C.H. and G.B. Sample alignment and mounting for the neutron scattering experiment was realized by R.S. and N.G. Neutron scattering experiments were carried out by R.S. and N.G. with J.O. and B.W. as local contacts. U.F. built the polarization neutron analyser used for the HYSPEC experiment. The experimental data were analysed by N.G., R.S., T.F. and M.K. Calculations were made by H.Y. and N.S. The paper was written by R.S. with feedback from all authors.

### Competing interests

The authors declare no competing interests.

Correspondence to Romain Sibille.

## Supplementary information

1. ### Supplementary Information

Supplementary Figures 1–4, Supplementary References

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