Entanglement, tensor networks and black hole horizons

Javier Molina-Vilaplana

Universidad Politécnica de Cartagena

We investigate a recent conjecture connecting the AdS/CFT correspondence and entanglement renormalization tensor network states (MERA). The proposal interprets the tensor connectivity of the MERA states associated to quantum many body systems at criticality, in terms of a dual holographic geometry which accounts for the qualitative aspects of the entanglement and the correlations in these systems. In this work, we propose a simple MERA tensor network to describe quantum critical systems at finite temperature. In the AdS/CFT, the gravity dual of a finite temperature state is the well-known AdS black hole in which the inverse temperature of the system is related with the distance of the boundary CFT to the black hole horizon. It has been argued that, inspired by the thermofield double construction of the eternal black hole, a MERA network with an horizon may be described by doubling the standard MERA for a pure state and then connecting together the infrared regions of both networks through a gluing-through-entanglement (GTE) operation. We show that the GTE operation may be satisfactorily characterized in terms of Matrix Product Density Operators (MPDO) and their purificatons.