The Kagome Lattice Heisenberg Model is one of the simplest realistic spin models with a quantum spin-liquid ground state. We discuss the current status of our understanding of this well-studied model. The precise nature of the spin-liquid state and the existence of a spin-gap in the model still remain in dispute. We also discuss experimental studies of Herbertsmithite material Kagome-antiferromagnet ZnCu_3(OH)_6Cl_2. We focus on NMR measurements by Imai and collaborators, who have presented strong evidence for a spin-gap in the excitation spectra. Through a Numerical Linked Cluster (NLC) calculation of the frequency moments, we show that despite the existence of substitutional disorder in these materials, the high temperature nuclear relaxation rates are well described by the Heisenberg model.
The 2016 Nobel Prize in Physics to Kosterlitz, Thouless and Haldane honors a new set of ideas and theoretical formalism that has gradually become the mainstay of modern condensed matter thinking. Quantum Field Theory, Topology and the Renormalization Group, lie at the heart of present day theory of condensed matter. The Kosterlitz-Thouless theory of phase transitions and Haldane's conjecture on the spin dependence of spectrum of spin-chains were two of the most influential works in bringing these ideas together. These along with the Thouless-Kohmoto-Nightingale-Den Nijs-(TKNN) work on topological invariants of band structures were duly recognized by the Nobel committee. This talk will discuss how these theories defied existing paradigms and no-go theorems. And, how they continue to play a huge role in how we address quantum phases and phase transitions today. This Nobel Prize potentially sets the stage for many more prizes in the field of Topological Matter.