Representability of Critical Phenomena in 2D Isometric Tensor Networks

Isometric tensor networks (isoTNS) are a generalization of the canonical form of matrix product states in one dimension to tensor networks in higher dimensions. Recently it has been shown that many interesting two-dimensional quantum many-body states, such as topologically ordered states, can be represented exactly as an isoTNS, and numerical work has shown that these tensor networks can be optimized efficiently. However, the full class of quantum states which can be represented by isoTNS remains poorly understood. We make progress on this question by constructing isoTNS from cellular automata, revealing a surprisingly rich variational power of this ansatz.