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


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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