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Spin ice magnetic monopoles are fractionalized emergent excitations in aclass of frustrated magnets called spin ices. The classical spin ice model hasan extensive number of ground state spin configurations, whereas magneticmonopoles can be thought of as the endpoints of string operators applied tothese ground states. Introducing quantum fluctuations into the model inducesmonopoles with dynamics, which would normally lift the degeneracy of thetwo-monopole energy level at the linear order of the perturbation. Contrary tothis expectation, we find that quantum fluctuations in the form of a locallytransverse field term partially preserve the extensive degeneracy of themonopole pairs up to the much weaker splitting of the background monopole-freespin ice configurations. Each of these approximately degenerate excited states,termed mesons, can be represented as a bound monopole-antimonopole pairdelocalized in a classical spin ice background.

Mesonic excited states of magnetic monopoles in quantum spin ice