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We develop a non-perturbative "gauge Mean Field Theory" (gMFT) method tostudy a general effective spin-1/2 model for magnetism in rare earthpyrochlores. gMFT is based on a novel exact slave-particle formulation, andmatches both the perturbative regime near the classical spin ice limit and thesemiclassical approximation far from it. We show that the full phase diagramcontains two exotic phases: a quantum spin liquid and a coulombic ferromagnet,both of which support deconfined spinon excitations and emergent quantumelectrodynamics. Phenomenological properties of these phases are discussed.

Coulombic Quantum Liquids in Spin-1/2 Pyrochlores