Just in time for the holiday season, I have received the news that two of our papers have been accepted for publication. The first one, in collaboration with Matthew Cha and Bruno Nachtergaele is on the stability of superselection sectors under perturbations of the dynamics. It is already available online and will appear in Communications in Mathematical Physics with doi 10.1007/s00220-019-03630-1. A summary of the main results in this paper can be found here on my website.

The other paper, with Kohtaro Kato, is already available online at Journal of Physics A: Mathematical and Theoretical. In this paper we define a new invariant for ground states of local commuting projector codes with topological order. In contrast with the stability result mentioned above, here we consider finite dimensional systems. The invariant, which in principle can be calculated locally, is related to the appearance of superselection sectors, and coincides with the quantum dimension in interesting cases such as Kitaev’s quantum double model. In the paper we show that it indeed is invariant under finite depth quantum circuits, using results first obtained by Haah. This work is partly motivated by my work with Leander Fiedler and Tobias Osborne, about which I wrote earlier here.