Entanglement phase transitions from holographic random tensor networks

In this talk, I will discuss new types of quantum phase transitions between area-law and volume-law entangled states. An example of such an entanglement phase transition is provided by the many-body localization transition in disordered quantum systems that separates a thermalizing phase at weak disorder from a many-body localized phase at strong disorder where statistical mechanics breaks down. In the spirit of random matrix theory, I will describe a simple model for such transitions where a physical quantum spin system lives at the (“holographic”) boundary of a bulk random tensor network. By mapping the calculation of the entanglement properties of the boundary system onto a classical statistical mechanics model, I will argue that one can get an analytic handle on the field theory of these entanglement transitions.

Joint work with Andreas W.W. Ludwig, Andrew C. Potter and Yi-Zhuang You.