Entanglement, Holography and Tensor Networks

In recent years, it has been proposed that the space-time fabric could emerge from the entanglement patterns within the degrees of freedom of a dual quantum many body theory.

These ideas have a natural arena to play with in the field of tensor networks. There are many different types of tensor networks, but those on which much interest has been raised is MERA (multi-scale entanglement renormalization ansatz). Namely, it has been noted that the entanglement patterns within a quantum state given by a MERA tensor network, resemble the structure of entanglement in AdS/CFT evinced by the Ryu-Takayanagi formula. This has led to the proposal that MERA could be realization of this duality. Motivated, by this, a (non)perturbative MERA formalism, able to deal with continuous interacting theories, seems to be essential to advance in this program.

Here, we will briefly introduce a MERA formalism for interacting quantum field theories (icMERA). Our results show that icMERA wavefunctionals encode proper non-Gaussian correlations of an interacting theory, thus providing a new variational tool to study the connection between tensor networks and holography.