Entanglement Transitions in Tree Tensor Networks

Entanglement transitions are a new class of phase transitions between states of low (e.g. area-law) entanglement and high (e.g. volume-law) entanglement. The many-body localization transition separating localized eigenstates and thermal eigenstates is an example of such, and interest in MBL inspired the creation of more tractable models featuring entanglement transitions, such as ensembles of "random tensor network states", the focus of this talk. These allow for an exact mapping to statistical mechanics models, but with a difficult to analyze replica limit. I will discuss features of entanglement transitions in a subclass of these models in which the tensor networks have tree geometries and various patterns of disorder, allowing for easier numerical and analytical analysis, drawing connections to results seen in other models of entanglement transitions along the way.

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