Lars Onsager Prize Talk: Quantum phase transitions in quantum matter

I will survey examples of quantum phase transitions, with applications to experiments on a variety of quantum materials. The simplest examples are associated with symmetry-breaking order parameters. More subtle examples involve emergent gauge fields, and their confinement or Higgs transitions, sometimes accompanied by changes in the volume enclosed by the Fermi surface. General aspects of the non-zero temperature dynamics of quantum critical systems will be noted, along with holographic connections to the dynamics of black holes. I will conclude by discussing the phase diagram of the hole-doped cuprate superconductors, and ideas on the transformations near optimal doping.