Disordered, Spin Liquid and Valence-Bond Ordered Phases of the Kagome Lattice Quantum Ising Models With Transverse Field and XXZ Dynamics

TL;DR

This paper explores the conditions under which disordered, spin liquid, and valence-bond ordered phases emerge in Kagome lattice quantum Ising models with transverse field and XXZ dynamics, using analytical methods.

Contribution

It demonstrates how various quantum dynamical processes can produce all three phases, especially highlighting the RVB liquid and valence-bond ordered states in Kagome systems.

Findings

Resonant valence bond (RVB) liquid phase with short-ranged correlations identified.

Valence-bond ordered phase compatible with gapless singlet states proposed for Kagome Heisenberg antiferromagnet.

Analytical framework combining gauge theory, duality, and variational methods developed.

Abstract

General conditions in which disordered, spin liquid, and valence-bond ordered phases occur in quantum Ising antiferromagnets are studied using the prototype Kagome lattice spin models. A range of 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 (RVB) 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.