An entanglement perspective on generalized symmetries, dualities and anomalies

One of the big challenges in the field of quantum technologies is the understanding of strongly correlated quantum many-body systems. Tensor networks have played a crucial role in elucidating the essential role of symmetries in quantum matter, leading among other things to the classification of 1+1D symmetry-protected topological phases and a comprehensive understanding of 2+1D topological quantum order. The central goal of this project is to extend these results to incorporate spatial and higher-form symmetries in this formalism. Our first objective is to study the full classification of 2+1D topological phases protected by space group symmetries in PEPS. We construct representative PEPS ansätze for each of these phases that can be used as the basis for numerical simulations of physically relevant models in which these spatial symmetries are omnipresent. We will construct scaling theories and study edge theories. Discrete matrix product operator algebras will be generalized to include continuous symmetries, anomalies and quantum group symmetries, and will be used to construct explicit intertwiners for dual theories. Subsequently, we will simulate field theories with 1-form symmetries. Finally, we will tackle the issue of describing 3+1D topological orders in terms of tensor networks, in which a holographic reduction is then used to study higher-form symmetries in lower dimensional lattice models.