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

The entanglement entropy of a pure quantum state of a bipartite system is defined as the von Neumann entropy of the reduced density matrix obtained by tracing over one of the two parts. Critical ground states of local Hamiltonians in one dimension have an entanglement entropy that diverges logarithmically in the subsystem size, with a universal coefficient that is is related to the central charge of the associated conformal field theory. Here I will discuss recent extensions of these ideas to a class of quantum critical points with dynamic critical exponent $z=2$ in two space dimensions and to 2D systems in a topological phase. The application of these ideas to quantum dimer models and fractional quantum Hall states will be discussed.