MIT

Title: Kagome lattice antiferromagnets: A quest for unconventional quantum phases

Abstract: Geometrically frustrated quantum magnets hold a very important role in the active search for exotic quantum phases and spin liquids. Quantum liquid, with topological order and fractionalized excitations, arising from only the nearest neighbor exchange has not yet been ruled out in the Kagome and pyrochlore antiferromagnets, unlike in many others that initially had been looked upon with great hope. In this talk I will discuss the picture of quantum phases in the Kagome lattice Heisenberg and Ising models that is provided by the Z2 and U(1) lattice gauge theories. The Heisenberg model has been studied numerically by means of exact diagonalization, and it has been suggested that an exotic spin liquid with a gapless band of singlet excitations is realized in this system. I will compare these numerical results with a theoretical proposal of a complicated valence bond ordered phase, and argue that the Kagome quantum Heisenberg model might be a long-range ordered paramagnet. I will also present analysis of possible phases in the quantum Ising models on the Kagome lattice with various types of spin dynamics. A weak transverse field, and other perturbations that do not conserve total spin, give rise to a non-topological disordered quantum phase, and in some circumstances a valence bond ordered and magnetized phase (responsible for a plateau in the magnetization curve).