Mathematics Colloquia and Seminars

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Several years ago, Nayak and Else argued that Symmetry Protected Topological phases in d dimensions can be classified using non-on-site actions of the symmetry group in d-1 dimensions. Such non-on-site actions can have an “anomaly”, in the sense that the symmetry action cannot be consistently localized. Nayak and Else assumed that the symmetry group is finite and the non-on-site action is given by a finite-depth local unitary circuit. I will explain how to generalize the construction of the anomaly index in two directions: to Lie groups as well as to arbitrary actions which preserve locality. I will show that certain anomalies, including the U(1) anomaly of chiral modes of quantum Hall systems, cannot arise in lattice spin chains. I will also discuss some dynamical consequences of a non-vanishing anomaly index and state a general theorem which includes Lieb-Schultz-Mattis-type theorems as a special case.