Disordered, spin liquid, and valence-bond ordered phases of kagome lattice quantum Ising models with transverse field and XXZ dynamics -: art. no. 064423

We study general conditions in which disordered, spin liquid, and valence-bond ordered phases occur in the Kagome lattice quantum Ising antiferromagnets. Different quantum dynamical processes in the Ising model, with and without total Ising spin conserved, are analytically shown to yield all three characteristic quantum paramagnetic phases in the Kagome system. Special emphasis is given to the XXZ model that can be sensibly compared to the Kagome lattice Heisenberg antiferromagnet. It is explicitly demonstrated that the total-spin-conserving dynamics can yield a resonant valence bond liquid phase with very short-ranged correlations, but also a valence-bond ordered phase compatible with the one proposed to explain the seemingly gapless singlet states of the Heisenberg antiferromagnet on the Kagome lattice. Likely consequences for generic spin models are discussed. The analysis combines compact U(1) gauge theory, duality transformations, lattice-field-theoretical methods, and variational approach.