It's the Symmetry, Stupid: Gearing Up Tensor Networks for the Topological Quantum Revolution

A bird's-eye point of view of the central objectives of this grant are:

1. To use the language of tensor networks to synthesize the mathematical structures obtained in the context of integrable spin systems, conformal field theory, topological field theory and tensor categories, and to use that characterization to study topological and/or critical phases of matter.

2. To develop a powerful variational tensor network toolbox incorporating non-local / categorical / non-invertible symmetries, unravel the entanglement structure of different phases of quantum many body systems, both for the case of lattice systems and of quantum field theories.

3. To use this toolbox to construct state of the art renormalization group flows for interacting systems, both on the lattice and in the continuum.

4. To use tensor networks to construct and analyse novel quantum error correcting codes, and study the relationship between error correction, entanglement, the holographic principle and renormalization.