The gauging of a global symmetry, that is, promoting it from global to local by adding new degrees of freedom, the gauge fields, plays a key role in physics: It is the origin of the fundamental interactions in the Standard Model. Very successful gauging procedures have been proposed at the level of states, for the case of global on-site symmetries where the action is identical and independent in every part of the system. However, in quantum systems there can be obstructions to gauging a global symmetry, in which case the symmetry is dubbed anomalous. Such obstructions are related to the fact that the global symmetry is not on-site. 

In their new paper in Physical Review B, our group members José Garre Rubio and Ilya Kull study non-on-site symmetries that have an additional structure: they take the form of a matrix product operator (MPO). They exploit the tensor network structure of the MPOs to construct local operators from them which satisfy the same group relations, even for anomalous MPOs. For non-anomalous MPOs, they use these local operators to explicitly gauge the MPO symmetry of a one-dimensional quantum state to obtain non-trivial gauged states. Importantly, this gauging procedure satisfies all the desired properties, just as the standard gauging for on-site symmetries does. They also show how this procedure is naturally represented in matrix product states protected by MPO symmetries, using the recent work arXiv:2203.12563 (to appear in Quantum). Finally, in the case of anomalous MPOs, their work sheds light on the obstructions to gauging these symmetries.

For more details, we encourage you to have a look at the paper, either on arXiv (open access) or at the published version in Phys. Rev. B 107, 075137 (2023).

 This work has received support through the ERC grant SEQUAM.