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The entanglement entropy of a pure quantum state of a bipartite system $A\cup B$ is defined as the von Neumann entropy of the reduced density matrixobtained by tracing over one of the two parts. Critical ground states of localHamiltonians in one dimension have entanglement that diverges logarithmicallyin the subsystem size, with a universal coefficient that for conformallyinvariant critical points is related to the central charge of the conformalfield theory. We find the entanglement entropy for a standard class of $z=2$quantum critical points in two spatial dimensions with scale invariant groundstate wave functions: in addition to a nonuniversal ``area law'' contributionproportional to the size of the $AB$ boundary, there is generically a universallogarithmically divergent correction. This logarithmic term is completelydetermined by the geometry of the partition into subsystems and the centralcharge of the field theory that describes the equal-time correlations of thecritical wavefunction.Comment: 4 pages, 1 figure, 28 reference

Entanglement Entropy of 2D Conformal Quantum Critical Points: Hearing the Shape of a Quantum Drum