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General conditions in which disordered, spin liquid, and valence-bond orderedphases occur in quantum Ising antiferromagnets are studied using the prototypeKagome lattice spin models. A range of quantum dynamical processes in the Isingmodel, with and without total Ising spin conserved, are analytically shown toyield all three characteristic quantum paramagnetic phases in the Kagomesystem. Special emphasis is given to the XXZ model that can be sensiblycompared to the Kagome lattice Heisenberg antiferromagnet. It is explicitlydemonstrated that the total-spin-conserving dynamics can yield a resonantvalence bond (RVB) liquid phase with very short-ranged correlations, but also avalence-bond ordered phase compatible with the one proposed to explain theseemingly gapless singlet states of the Heisenberg antiferromagnet on theKagome lattice. Likely consequences for generic spin models are discussed. Theanalysis combines compact U(1) gauge theory, duality transformations,lattice-field-theoretical methods, and variational approach.Comment: 24 pages, 23 figure

physical review. b, condensed matter and materials physics

Disordered, spin liquid, and valence-bond ordered phases of kagome lattice quantum Ising models with transverse field and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>X</mml:mi><mml:mi>X</mml:mi><mml:mi>Z</mml:mi></mml:mrow></mml:math>dynamics

Disordered, spin liquid, and valence-bond ordered phases of kagome lattice quantum Ising models with transverse field andXXZdynamics