Condensed Matter Theory Seminar: Zhicheng Yang, University of Maryland, “Entanglement phase transitions in random stabilizer tensor networks”

We explore entanglement phase transitions in a class of random tensor network models with “stabilizer” local tensors which we name Random Stabilizer Tensor Networks (RSTNs). For RSTNs defined on a two-dimensional square lattice, we 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, we find that there exists a critical measurement rate p_c for each D<\em> &8805; 3 above which the boundary state becomes area-law entangled. We 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. Our 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. We 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.
Host: Meng Cheng (m.cheng@yale.edu)
Please contact Taylor Dunnigan (taylor.dunnigan@yale.edu) for zoom information.