Entanglement Wedges from the Information Metric in Conformal Field Theories.

We present a new method of deriving the geometry of entanglement wedges in holography directly from conformal field theories (CFTs). We analyze an information metric called the Bures metric of reduced density matrices for locally excited states. This measures the distinguishability of states with different points excited. For a subsystem given by an interval, we precisely reproduce the expected entanglement wedge for two-dimensional holographic CFTs from the Bures metric, which turns out to be proportional to the anti-de Sitter metric on a time slice. On the other hand, for free scalar CFTs, we do not find any sharp structures like entanglement wedges. When a subsystem consists of two disconnected intervals, we manage to reproduce the expected entanglement wedge from holographic CFTs with the correct phase transitions, up to a very small error, from a quantity alternative to the Bures metric.

Entanglement of Purification in Many Body Systems and Symmetry Breaking.

We study the entanglement of purification (EOP), a measure of total correlation between two subsystems A and B, for free scalar field theory on a lattice and the transverse-field Ising model by numerical methods. In both of these models, we find that the EOP becomes a nonmonotonic function of the distance between A and B when the total number of lattice sites is small. When it is large, the EOP becomes monotonic and shows a plateaulike behavior. Moreover, we also show that the original reflection symmetry which exchanges A and B can get broken in optimally purified systems. We provide an interpretation of our results in terms of the interplay between classical and quantum correlations.

Holographic Entanglement of Purification from Conformal Field Theories.

We explore a conformal field theoretic interpretation of the holographic entanglement of purification, which is defined as the minimal area of the entanglement wedge cross section. We argue that, in AdS_{3}/CFT_{2}, the holographic entanglement of purification agrees with the entanglement entropy for a purified state, obtained from a special Weyl transformation, called path-integral optimizations. By definition, this special purified state has minimal path-integral complexity. We confirm this claim in several examples.