Quantum magnetism and criticality

Magnetic insulators have proved to be fertile ground for studying new types of quantum many-body state, and I survey recent experimental and theoretical examples. The insights and methods also transfer to novel superconducting and metallic states. Of particular interest are critical quantum states, sometimes found at quantum phase transitions, which have gapless excitations with no particle- or wave-like interpretation, and control a significant portion of the finite-temperature phase diagram. Remarkably, their theory is connected to holographic descriptions of Hawking radiation from black holes.