On Short Ranged Resonating Valence Bond Liquids

Over 40 years ago, P W Anderson proposed the short ranged resonating valence bond state as an alternative to Neel order in antiferromagnets with strong fluctuations---in hindsight, the first proposal for a topologically ordered $Z_2$ spin liquid. In the last year, convincing numerical evidence has accumulated for the existence of such $Z_2$ spin liquids in short ranged Hamiltonians on simple lattices in two dimensions. I will sketch the intellectually productive historical route between these two developments and survey what we now know about the physics of the short ranged RVB and allied states of matter.