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

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• Frustrated magnetism
• Magnetic order
• Quantum spin liquid
• Spin ice