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Quantum spin liquids (QSL) have generated considerable excitement as phasesof matter with emergent gauge structures and fractionalized excitations. Inthis context, phase transitions out of QSLs have been widely discussed as Higgstransitions from deconfined to confined phases of a lattice gauge theory.However the possibility of a wider range of novel phases, occuring betweenthese two limits, has yet to be systematically explored. In this Letter, wedevelop a formalism which allows for interactions between fractionalisedquasiparticles coming from the constraint on the physical Hilbert space, andcan be used to search for exotic, hidden phases. Taking pyrochlore spin ice asa starting point, we show how a U(1) QSL can give birth to abundant daughterphases, without need for fine--tuning of parameters. These include a(charged--) $\mathbb{Z}_2$ QSL, and a supersolid. We discuss implications forexperiment, and numerical results which support our analysis. These results areof broad relevance to QSL subject to a parton description, and offer a newperspective for searching exotic hidden phases in quantum magnets.

Hidden phases born of a quantum spin liquid: Application to pyrochlore spin ice