Quantum criticality and high temperature superconductivity

Many modern materials, including the high temperature superconductors, display quantum critical points where the electron wavefunction is “entangled”, so that the low energy excitations cannot be described in a quasiparticle basis. I will describe recent progress in understanding the physics of such critical points, using quantum field theory, string theory, and quantum Monte Carlo simulations. I argue that these advances shed light on many of the puzzling features of the phase diagrams of the high temperature superconductors.