Theory of the Kagome Lattice Ising Antiferromagnet in Weak Transverse Field

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We study the quantum Ising antiferromagnet on the Kagome lattice, with weak transverse field dynamics and other local perturbations. We analytically demonstrate the possibility of a disordered zero-temperature phase that is smoothly connected to the phase at strong transverse fields. This is done by means of an appropriate mapping to a compact U(1) gauge theory on the honeycomb lattice that is coupled to a charge-1 matter field. Our results are consistent with existing Monte-Carlo calculations. The differences with other commonly studied lattices (in which such disordered phases do not obtain at weak transverse fields) is explained. Ordered phases are also shown to be possible in principle in the weak transverse field limit, and are briefly studied.