Entanglement phase transitions in random stabilizer tensor networks
Abstract
We explore a class of random tensor network models with ``stabilizer'' local tensors which we name Random Stabilizer Tensor Networks (RSTNs). For RSTNs defined on a twodimensional square lattice, we perform extensive numerical studies of entanglement phase transitions between volumelaw and arealaw entangled phases of the onedimensional boundary states. These transitions occur 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. In the absence of broken bonds, we find that the RSTN supports a volumelaw entangled boundary state with bond dimension $D\geq3$ where $D$ is a prime number, and an arealaw entangled boundary state for $D=2$. Upon breaking bonds at random in the bulk with probability $p$, there exists a critical measurement rate $p_c$ for each $D\geq 3$ above which the boundary state becomes arealaw entangled. To explore the conformal invariance at these entanglement transitions for different prime $D$, we consider tensor networks on a finite rectangular geometry with a variety of boundary conditions, 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 volumelaw phase and demonstrate quantitative agreement with the recently proposed description in terms of a directed polymer in a random environment.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.12376
 Bibcode:
 2021arXiv210712376Y
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Disordered Systems and Neural Networks;
 High Energy Physics  Theory;
 Quantum Physics
 EPrint:
 29 pages, 20 figures