Experimental signatures of emergent quantum electrodynamics in Pr$_2$Hf$_2$O$_7$

TL;DR

This paper presents neutron scattering evidence that Pr$_2$Hf$_2$O$_7$ exhibits a quantum spin ice state, showing signatures of emergent quantum electrodynamics with fractionalized excitations and magnetic photon-like modes.

Contribution

First experimental evidence of a three-dimensional quantum spin ice state demonstrating emergent quantum electrodynamics in Pr$_2$Hf$_2$O$_7$.

Findings

Observation of pinch points indicating classical spin ice behavior

Suppression of pinch points consistent with quantum coherence

Detection of a continuum of inelastic spin excitations resembling fractionalized particles

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 scales [1-2]. Such phases offer promising perspectives for device applications in quantum information technologies, and their study can reveal fundamentally novel 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 theory [3-7]. 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 Pr$_2$Hf$_2$O$_7$ 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 Pr$_2$Hf$_2$O$_7$ 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 which has so far mostly been explored in lower dimensionalities.