The speaker and his research group explore entanglement phase transitions in a class of random tensor network models with “stabilizer” local tensors which they named as Random Stabilizer Tensor Networks (RSTNs). For RSTNs defined on a two-dimensional square lattice, they find that the one-dimensional boundary state undergoes a transition from volume-law to area-law entangled, when either (a) the bond dimension D of the constituent tensors is varied, or (b) the tensor network is subject to random breaking of bulk bonds, implemented by forced measurements. Upon breaking bonds at random in the bulk with probability p, they find that there exists a critical measurement rate pc for each D≥ 3 above which the boundary state becomes area-law entangled. They further demonstrate the conformal invariance at the critical points and extract universal operator scaling dimensions via extensive numerical calculations of the entanglement entropy, mutual information and mutual negativity at their respective critical points. Their results at large D approach known universal data of percolation conformal field theory, while showing clear discrepancies at smaller D, suggesting a distinct entanglement transition universality class for each prime D. They further study universal entanglement properties in the volume-law phase and demonstrate quantitative agreement with the recently proposed description in terms of a directed polymer in a random environment.
