Entanglement at stronglyinteracting quantum critical points in 2+1D Speaker(s): Roger Melko
Abstract: In two or more spatial dimensions, leadingorder contributions to the scaling of entanglement entropy typically follow the "area" or boundary law. Although this leadingorder scaling is nonuniversal, at a quantum critical point (QCP), the subleading behavior does contain universal physics. Different universal functions can be access through entangling regions of different geometries. For example, for polygonal shaped regions, quantum field theories have demonstrated that the subleading scaling is logarithmic, with a universal coefficient dependent on the number of vertices in the polygon. Although such universal quantities are routinely studied in noninteracting field theories, it often requires numerical simulation to access them in interacting theories. In this talk, I discuss quantum Monte Carlo (QMC) and numerical LinkedCluster Expansion (NLCE) calculations of the Renyi entropies at the transversefield Ising model QCP on the 2D square lattice. We calculate the universal coefficient of the vertexinduced logarithmic scaling term, and compare to noninteracting field theory calculations by Casini and Huerta. Also, we examine the shape dependence of the Renyi entropy for finitesize toroidal lattices with smooth boundaries. Such geometries provide a sensitive probe of the gapless wave function in the thermodynamic limit, and give new universal quantities that could be examined by future fieldtheoretical studies in 2+1D.
Date: 10/05/2013  4:00 pm
Collection: Emergence & Entanglement II 2013
