Entanglement transitions in translation-invariant tensor networks

Recent studies of random tensor networks and quantum circuits led to the discovery of entanglement phase transitions in which the time evolving or boundary state changes from area law to volume law entanglement. In this work we explore the entanglement properties of the boundary state of a translationally invariant two dimensional tensor network, allowing us to use an infinite matrix product state approach to contract it row by row. Preliminary finite entanglement scaling analysis gives evidence for an entanglement transition that can be tuned either by (i) the virtual bond dimension (ii) the unitarity of the transfer matrix. Translational invariance means that row by row contraction defines an effective non unitary floquet evolution. Thus we conjecture that the entanglement transition is accompanied by a spectral transition of the transfer matrix akin to a transition to chaos.