We use low-depth quantum circuits, a specific type of tensor networks, to classify two-dimensional symmetry-protected topological many-body localized phases. For (anti)unitary onsite symmetries we show that the (generalized) third cohomology class of the symmetry group is a topological invariant; however, our approach leaves room for the existence of additional topological indices. We argue that our classification applies to quasiperiodic systems in two dimensions and systems with true random disorder within times which scale superexponentially with the inverse interaction strength. Our technique might be adapted to supply arguments suggesting the same classification for two-dimensional symmetry-protected topological ground states with a rigorous proof.

• Received 11 November 2019
• Revised 15 June 2020
• Accepted 16 June 2020

DOI:https://doi.org/10.1103/PhysRevB.102.014205