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Understanding the nature and behaviour of excitations in quantum spinliquids, and in topological phases of matter in general, is of fundamentalimportance and has proven crucial for experimental detection andcharacterisation of candidate materials. Current theoretical and numericaltechniques, however, have limited capabilities, especially when it comes tostudying gapped excitations. Here, we propose a semiclassical numerical methodto study systems whose spin liquid behaviour is underpinned by perturbativering-exchange Hamiltonians. Our method can readily access both thermodynamicand spectral properties. We focus in particular on quantum spin ice and itsphoton and vison excitations. After benchmarking the method against existingresults on photons, we use it to characterise visons and their thermodynamicbehaviour, which remained hitherto largely unexplored. We find that visons, incontrast to spinons in classical spin ice, form a weak electrolyte: vison pairsare the dominant population at low temperatures. This is reflected in thebehaviour of thermodynamic quantities, such as pinch point motifs in therelevant correlators. Visons also appear to strongly hybridise with the photonbackground, a phenomenon that affects the way these quasiparticles may show upin inelastic response measurements. Our results demonstrate that the method,and generalisations thereof, can substantially help our understanding ofquasiparticles and their interplay in quantum spin ice and other quantum spinliquids, quantum dimer models, and lattice gauge theories in general.

Seeing beyond the light: Vison and photon electrodynamics in quantum spin ice