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We study the S=1/2 Heisenberg antiferromagnet on the pyrochlore lattice inthe limit of strong easy-axis exchange anisotropy. We find, using only standardtechniques of degenerate perturbation theory, that the model has a U(1) gaugesymmetry generated by certain local rotations about the z-axis in spin space.Upon addition of an extra local interaction in this and a related model withspins on a three-dimensional network of corner-sharing octahedra, we can writedown the exact ground state wavefunction with no further approximations. Usingthe properties of the soluble point we show that these models enter the U(1)spin liquid phase, a novel fractionalized spin liquid with an emergent U(1)gauge structure. This phase supports gapped S^z = 1/2 spinons carrying the U(1)``electric'' gauge charge, a gapped topological point defect or ``magnetic''monopole, and a gapless ``photon,'' which in spin language is a gapless,linearly dispersing S^z = 0 collective mode. There are power-law spincorrelations with a nontrivial angular dependence, as well as novel U(1)topological order. This state is stable to ALL zero-temperature perturbationsand exists over a finite extent of the phase diagram. Using a convenientlattice version of electric-magnetic duality, we develop the effectivedescription of the U(1) spin liquid and the adjacent soluble point in terms ofGaussian quantum electrodynamics and calculate a few of the universalproperties. The resulting picture is confirmed by our numerical analysis of thesoluble point wavefunction. Finally, we briefly discuss the prospects forunderstanding this physics in a wider range of models and for making contactwith experiments.Comment: 22 pages, 14 figures. Further minor changes. To appear in Phys. Rev.

physical review. b, condensed matter and materials physics

Pyrochlore photons: The<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>U</mml:mi><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo><mml:mn /></mml:math>spin liquid in a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>1</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:mfrac></mml:math>three-dimensional frustrated magnet

Pyrochlore photons: TheU(1)spin liquid in aS=12three-dimensional frustrated magnet