PIRSA:15020134

Exact holographic mapping, tensor networks and space-time geometry

APA

Qi, X. (2015). Exact holographic mapping, tensor networks and space-time geometry. Perimeter Institute. https://pirsa.org/15020134

MLA

Qi, Xiao-Liang. Exact holographic mapping, tensor networks and space-time geometry. Perimeter Institute, Feb. 27, 2015, https://pirsa.org/15020134

BibTex

          @misc{ pirsa_15020134,
            doi = {},
            url = {https://pirsa.org/15020134},
            author = {Qi, Xiao-Liang},
            keywords = {Condensed Matter, Quantum Fields and Strings},
            language = {en},
            title = {Exact holographic mapping, tensor networks and space-time geometry},
            publisher = {Perimeter Institute},
            year = {2015},
            month = {feb},
            note = {PIRSA:15020134 see, \url{https://pirsa.org}}
          }
          

Abstract

Holographic duality is a duality between gravitational systems and non-gravitational systems. In this talk, I will propose a different approach for understanding holographic duality named as the exact holographic mapping. The key idea of this approach can be summarized by two points: 1) The bulk theory and boundary theory are related by a unitary mapping in the Hilbert space. 2) Space-time geometry is determined by the structure of correlations and quantum entanglement in a quantum state. When applied to lattice systems, the holographic mapping is defined by a unitary tensor network. For free fermion boundary theories, I will discuss how different bulk geometries are obtained as dual theories of different boundary states. A particularly interesting case is the AdS black hole geometry and the interpretation of the interior of a black hole. We will also discuss dual geometries of topological states of matter.