PIRSA:23120054

Anomalous symmetries of spin chains

Kapustin, A. (2023). Anomalous symmetries of spin chains. Perimeter Institute. https://pirsa.org/23120054

Kapustin, Anton. Anomalous symmetries of spin chains. Perimeter Institute, Dec. 19, 2023, https://pirsa.org/23120054 

          @misc{ pirsa_PIRSA:23120054,
            doi = {10.48660/23120054},
            url = {https://pirsa.org/23120054},
            author = {Kapustin, Anton},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Anomalous symmetries of spin chains},
            publisher = {Perimeter Institute},
            year = {2023},
            month = {dec},
            note = {PIRSA:23120054 see, \url{https://pirsa.org}}
          }

Anton Kapustin

California Institute of Technology (Caltech) - Division of Physics Mathematics & Astronomy

Talk number
PIRSA:23120054
Collection
Talk Type
Subject
Abstract

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. This anomaly is similar but distinct from ’t Hooft anomaly in QFT. 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. For simplicity, I will only discuss the one-dimensional case. One can prove that a nonzero anomaly index prohibits any invariant 1d Hamiltonian from having invariant ground states. This is similar to ’t Hooft anomaly matching in QFT. Lieb-Schultz-Mattis-type theorems arise as a special case where the symmetry group involves translations. This is joint work with Nikita Sopenko.

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