Tensor Network Representation for Decohered Error Correction Codes

Tensor networks are powerful tools for understanding pure-state systems with long-range entanglement, such as topological and fracton phases. Recently, it has been discovered that mixed states can also exhibit exotic topological properties that have no counterparts in pure states. In this work, we show that these intrinsically mixed states can be naturally represented using tensor networks, enabling both efficient simulations as well as deeper understandings of such states. We focus on intrinsically mixed phases based on pure-state error correction codes with various types of added decoherence or quenched disorder. Specifically, we construct explicit tensors for locally purifiable density operators across a wide range of fixed-point states and demonstrate that the tensor network remains invariant under entanglement renormalization group transformations.