Mesonic excited states of magnetic monopoles in quantum spin ice

Spin ice magnetic monopoles are fractionalized emergent excitations in a class of frustrated magnets called spin ices. The classical spin ice model has an extensive number of ground state spin configurations, whereas magnetic monopoles can be thought of as the endpoints of string operators applied to these ground states. Introducing quantum fluctuations into the model induces monopoles with dynamics, which would normally lift the degeneracy of the two-monopole energy level at the linear order of the perturbation. Contrary to this expectation, we find that quantum fluctuations in the form of a locally transverse field term partially preserve the extensive degeneracy of the monopole pairs up to the much weaker splitting of the background monopole-free spin ice configurations. Each of these approximately degenerate excited states, termed mesons, can be represented as a bound monopole-antimonopole pair delocalized in a classical spin ice background.