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The entanglement entropy of a pure quantum state of a bipartite system isdefined as the von Neumann entropy of the reduced density matrix obtained bytracing over one of the two parts. Critical ground states of local Hamiltoniansin one dimension have an entanglement entropy that diverges logarithmically inthe subsystem size, with a universal coefficient that is is related to thecentral charge of the associated conformal field theory. Here I will discussrecent extensions of these ideas to a class of quantum critical points withdynamic critical exponent $z=2$ in two space dimensions and to 2D systems in atopological phase. The application of these ideas to quantum dimer models andfractional quantum Hall states will be discussed.

Scaling of Entanglement Entropy at 2D quantum Lifshitz fixed points and topological fluids