We consider the special case of random tensor networks (RTNs) endowed with gauge symmetry constraints on each tensor. We compute the Rényi entropy for such states and recover the Ryu-Takayanagi (RT) formula in the large-bond regime. The result provides first of all an interesting new extension of the existing derivations of the RT formula for RTNs. Moreover, this extension of the RTN formalism brings it in direct relation with (tensorial) group field theories (and spin networks), and thus provides new tools for realizing the tensor network/geometry duality in the context of background-independent quantum gravity, and for importing quantum gravity tools into tensor network research.
Ryu-Takayanagi formula for symmetric random tensor networks / Chirco, G.; Oriti, D.; Zhang, M.. - In: PHYSICAL REVIEW D. - ISSN 2470-0010. - 97:12(2018). [10.1103/PhysRevD.97.126002]
Ryu-Takayanagi formula for symmetric random tensor networks
Chirco G.;Oriti D.;
2018
Abstract
We consider the special case of random tensor networks (RTNs) endowed with gauge symmetry constraints on each tensor. We compute the Rényi entropy for such states and recover the Ryu-Takayanagi (RT) formula in the large-bond regime. The result provides first of all an interesting new extension of the existing derivations of the RT formula for RTNs. Moreover, this extension of the RTN formalism brings it in direct relation with (tensorial) group field theories (and spin networks), and thus provides new tools for realizing the tensor network/geometry duality in the context of background-independent quantum gravity, and for importing quantum gravity tools into tensor network research.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.