An introduction to Quantum Spin Liquids

Abstract

Quantum spin liquids represent phases of condensed matter that fall beyond the paradigm of Landau’s symmetry based classification. They, instead, are characterized by the presence of subtle patterns of long-range many-body quantum entanglement. An ever growing list of experiments suggests that understanding such phases of matter forms a crucial step towards the development of a new and general framework of condensed matter systems. We provide an introduction to such physics in the context of quantum spin liquids that would be relevant to frustrated quantum magnets. We take two examples, (1) the two dimensional Z₂ quantum spin liquid in Kitaev’s Toric code model, and (2) the three dimensional U(1) quantum spin liquid in the XXZ pyrochlore system, both for spin$- \frac{1}{2}$ 1 2, to explain some of the inherent properties of quantum spin liquids, as we know them. The aim is to contrast these properties with those of conventional phases like the magnetically ordered ones. These differences range from novel excitations such as mutual semions in the form of Ising electric and magnetic charges in Toric code to emergent photons and fractionalized spin$- \frac{1}{2}$ excitations in XXZ pyrochlores. These two examples have been chosen to bring out the differences clearly, without going into the general structure of emergent gauge theories in quantum spin liquids. However, all the principles introduced here have very general applications.-