QUANTUM PHASE TRANSITIONS: FROM MOTT INSULATORS
TO THE CUPRATE SUPERCONDUCTORS

I begin with a discussion of the quantum theory of antiferromagnetism in Mott insulators. In one class of ground states, the electrons spins in such insulators are paired in valence bonds and there is an energy gap to all spin excitations. In a second class, there is a staggered static spin polarization on the lattice sites. I review experiments, simulations, and theories which have studied these phases, and the transitions between them. I will discuss the implications of this understanding of Mott insulators for recent experiments on the cuprate high temperature superconductors.