Entanglement at strongly-interacting quantum critical points


Melko, R. (2013). Entanglement at strongly-interacting quantum critical points. Perimeter Institute. https://pirsa.org/13110071


Melko, Roger. Entanglement at strongly-interacting quantum critical points. Perimeter Institute, Nov. 07, 2013, https://pirsa.org/13110071


          @misc{ pirsa_PIRSA:13110071,
            doi = {10.48660/13110071},
            url = {https://pirsa.org/13110071},
            author = {Melko, Roger},
            keywords = {},
            language = {en},
            title = {Entanglement at strongly-interacting quantum critical points},
            publisher = {Perimeter Institute},
            year = {2013},
            month = {nov},
            note = {PIRSA:13110071 see, \url{https://pirsa.org}}

Roger Melko University of Waterloo

Talk Type Conference


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.