27pRA-2 Holographic Geometry of Entanglement Renormalization in Quantum Field Theories

Masahiro Nozaki, Shinsei Ryu, Tadashi Takayanagi

Chanyong Park B, Chi‐Ok Hwang, Kyungchan Cho +1 more

For a given entanglement entropy of quantum field theory, we investigate how to reconstruct its dual geometry by applying the Ryu-Takayanagi formula and the deep learning method. In the holographic setup, the radial coordinate is identified with the energy scale of the dual quantum field theory. Therefore, the holographic dual geometry can describe how physical properties of a quantum field theory change along the renormalization group flow. Intriguingly, we show that the reconstructed geometry only from the entanglement entropy data can give us more information about other physical properties like thermodynamic quantities in the infrared region.

Agon Quintero, César A. Alfonso

Feng-Li Lin

Masahiro Nozaki A, Shinsei Ryu, Tadashi Takayanagi +1 more

We study a conjectured connection between AdS/CFT and a real-space quantum renormalization group scheme, the multi-scale entanglement renormalization ansatz (MERA). By making a close contact with the holographic formula of the entanglement entropy, we propose a general definition of the metric in the MERA in the extra holographic direction. The metric is formulated purely in terms of quantum field theoretical data. Using the continuum version of the MERA (cMERA), we calculate this emergent holographic metric explicitly for free scalar boson and free fermions theories, and check that the metric so computed has the properties expected from AdS/CFT. We also discuss the cMERA in a time-dependent background induced by quantum quench and estimate its corresponding metric.

Frank Verstraete