This question is investigated in a new paper in Physical Review B by Laurens Lootens, Bram Vancraeynest-De Cuiper, and Frank Verstraete from Ghent University, together with our group leader Norbert Schuch. In their work, they consider two topological models with equivalent topological data – so-called Morita-equivalent models. While these models exhibit equivalent topological excitations, it has hitherto been unknown whether this also means that the models can be related on a microscopic level.

In their work, Lootens et al. show that for Morita-equivalent topological models, there always exist a local, constant-depth unitary circuit which maps between those two models, and they provide an explicit construction for such a circuit. Notably, this circuit does not only map between the ground states of the models, but also between their excited states, and thus provides a local mapping between the topological excitations, i.e., anyons, of the two models.

To learn more, consult the paper at Physical Review B or on the arXiv.

This work has received support through the ERC grant SEQUAM.