Anomalous symmetries of quantum spin chains and generalization of LiebSchultzMattis theorem
Anomalous symmetries of quantum spin chains and generalization of LiebSchultzMattis theorem

Nikita Sopenko, IAS
Jadwin Hall A07
I will discuss how symmetries of quantum spin systems can be realized. For a given realization of a symmetry group G of a 1d spin system, I will define the anomalous index that takes values in the cohomology H^4(BG) of the classifying space of the group. I will show that a Ginvariant system with a nontrivial anomalous index can not have a gapped Ginvariant ground state, that provides a generalization of LiebSchultzMattis theorem when the translation symmetry is not necessarily present.