We introduce a generalised class of (symmetric) random tensor network states in the framework of group field theory. In this setting, we compute the Rényi entropy for a generic bipartite state via a mapping to the partition function of a topological 3D BF theory, realised as a simple interacting group field theory. The expectation value of the entanglement entropy is calculated by an expansion into stranded Feynman graphs and is shown to be captured by a Ryu-Takayanagi formula. For the simple case of a 3D BF theory, we can prove the linear corrections, given by a polynomial perturbation of the Gaussian measure, to be negligible for a broad class of networks.
Group field theory and holographic tensor networks: Dynamical corrections to the Ryu-Takayanagi formula / Chirco, G.; Goessmann, A.; Oriti, D.; Zhang, M.. - In: CLASSICAL AND QUANTUM GRAVITY. - ISSN 0264-9381. - 37:9(2020), p. 095011. [10.1088/1361-6382/ab7bb9]
Group field theory and holographic tensor networks: Dynamical corrections to the Ryu-Takayanagi formula
Chirco G.;Oriti D.;
2020
Abstract
We introduce a generalised class of (symmetric) random tensor network states in the framework of group field theory. In this setting, we compute the Rényi entropy for a generic bipartite state via a mapping to the partition function of a topological 3D BF theory, realised as a simple interacting group field theory. The expectation value of the entanglement entropy is calculated by an expansion into stranded Feynman graphs and is shown to be captured by a Ryu-Takayanagi formula. For the simple case of a 3D BF theory, we can prove the linear corrections, given by a polynomial perturbation of the Gaussian measure, to be negligible for a broad class of networks.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.