Entanglement Bootstrap and Conformal Field Theory

Entanglement Bootstrap is a research program to understand and extract the universal data of quantum many body states from local entanglement information.  Since this universal data is usually encoded in a quantum field theory, the program can teach us about QFT.  The program proceeds by identifying conditions satisfied by the reduced density matrix of a ball for a given class of fixed-point states.  After briefly reviewing what we've learned about the topological field theories that describe the low energy physics of liquid gapped states, I'll describe our progress at using this philosophy to learn about conformal field theory in 1+1 dimensions and above.  The talk is based on work with Xiang Li, Ting-Chun (David) Lin, and Rolando Ramirez Camasca.