Entanglement phase transitions from holographic random tensor networks

Ryan Levy, Bryan K. Clark

Zhi-Cheng Yang, Yaodong Li, Matthew P. A. Fisher +1 more

The authors explore a class of random tensor network models with stabilizer local tensors and study the entanglement phase transitions in these models. They find that an entanglement phase transition can be induced by randomly breaking bulk tensor legs and they extract a set of universal data characterizing the conformal invariance at the critical points. The results clearly demonstrate regimes where a geometric bond percolation picture does or does not apply at the transitions. This work may open new connections to holographic quantum error correcting codes, built from tensor networks.

Romain Vasseur, Andrew C. Potter, Yi‐Zhuang You +1 more

Universal features in patterns of entanglement of quantum states provide valuable information-theoretical insights into complex quantum many-body phases and dynamics. This work uncovers a novel class of phase transition between weakly- and strongly- entangled quantum states, described holographically at the boundary of a random tensor network. The univeral scaling structure of these transitions is explored via an exact mapping onto a classical spin model, which also opens the door to efficient numerical methods to study these complex quantum phenomena.

Alberto Faraggi, Leopoldo A. Pando Zayas, César Augusto Terrero-Escalante

Javier Abajo-Arrastia, João Aparício, Esperanza López

Chris Akers, Thomas Faulkner, Simon Lin +1 more

A bstract In holographic theories, the reflected entropy has been shown to be dual to the area of the entanglement wedge cross section. We study the same problem in random tensor networks demonstrating an equivalent duality. For a single random tensor we analyze the important non-perturbative effects that smooth out the discontinuity in the reflected entropy across the Page phase transition. By summing over all such effects, we obtain the reflected entanglement spectrum analytically, which agrees well with numerical studies. This motivates a prescription for the analytic continuation required in computing the reflected entropy and its Rényi generalization which resolves an order of limits issue previously identified in the literature. We apply this prescription to hyperbolic tensor networks and find answers consistent with holographic expectations. In particular, the random tensor network has the same non-trivial tripartite entanglement structure expected from holographic states. We furthermore show that the reflected Rényi spectrum is not flat, in sharp contrast to the usual Rényi spectrum of these networks. We argue that the various distinct contributions to the reflected entanglement spectrum can be organized into approximate superselection sectors. We interpret this as resulting from an effective description of the canonically purified state as a superposition of distinct tensor network states. Each network is constructed by doubling and gluing various candidate entanglement wedges of the original network. The superselection sectors are labelled by the different cross-sectional areas of these candidate entanglement wedges.