Tales from the Quantum Spin Liquid Crypt

Two-dimensional frustrated quantum antiferromagnets can harbor a phase of matter called a quantum spin liquid. This state exhibits no conventional symmetry but emergent, topological order. Remarkably, the spin liquid state has fascinating features such as gapped fractionalized quasiparticle excitations with exotic quantum statistics making it a highly sought after state in the (topological) quantum computation community.

In this talk, I will review properties of a spin liquid state and discuss the concept of quantum entanglement which is an important diagnostic tool when it comes to uncovering the nature of a spin liquid state. I will introduce a family of fractional quantum Hall (FQH) lattice states. Using the Moore-Read lattice state as an example, I will demonstrate how ''FQH physics in lattice systems'' can advance the field by discussing the issue of inserting quasiholes and quasielectrons into the FQH lattice state, the insertion of the latter being impossible in continuum FQH states because of a singularity problem.