Entanglement at strongly-interacting quantum critical points

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At a quantum critical point (QCP) in two or more spatial dimensions,
leading-order contributions to the scaling of entanglement entropy
typically follow the "area" law, while sub-leading behavior contains
universal physics.  Different universal functions can be access through
entangling subregions of different geometries.  For example, for
polygonal shaped subregions, quantum field theories have demonstrated
that the sub-leading scaling is logarithmic, with a universal
coefficient dependent on the number of vertices in the polygon. 
Although such universal quantities are routinely studied in
non-interacting field theories, it requires numerical simulation to
access them in interacting theories.  In this talk, we discuss numerical
calculations of the Renyi entropies at QCPs in 2D quantum lattice
models.  We calculate the universal coefficient of the vertex-induced
logarithmic scaling term, and compare to non-interacting field theory
calculations.  Also, we examine the shape dependence of the Renyi
entropy for finite-size lattices with smooth subregion boundaries. Such
geometries provide a sensitive probe of the gapless wavefunction in the
thermodynamic limit, and give new universal quantities that could be
examined by field-theoretical studies in 2+1D.