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Domain Wall Decorations, Anomalies and Spectral Sequences in Bosonic Topological Phases

Qing-Rui Wang Department of Physics, Yale University, New Haven, CT 06511-8499, USA Shang-Qiang Ning Department of Physics and HKU-UCAS Joint Institute for Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China Meng Cheng Department of Physics, Yale University, New Haven, CT 06511-8499, USA

arXiv subject: High Energy Physics - Theory (hep-th) arXiv subject: Strongly Correlated Electrons (cond-mat.str-el) mathscidoc:2206.74020

2021.4
In this work we investigate the decorated domain wall construction in bosonic group-cohomology symmetry-protected topological (SPT) phases and related quantum anomalies in bosonic topological phases. We first show that a general decorated domain wall construction can be described mathematically as an Atiyah-Hirzebruch spectral sequence, where the terms on the E2 page correspond to decorations by lower-dimensional SPT states at domain wall junctions. For bosonic group-cohomology SPT phases, the spectral sequence becomes the Lyndon-Hochschild-Serre (LHS) spectral sequence for ordinary group cohomology. We then discuss the physical interpretations of the differentials in the spectral sequence, particularly in the context of anomalous SPT phases and symmetry-enriched gauge theories. As the main technical result, we obtain a full description of the LHS spectral sequence concretely at the cochain level. The explicit formulae are then applied to explain Lieb-Schultz-Mattis theorems for SPT phases, and also derive a new LSM theorem for easy-plane spin model in a π flux lattice. We also revisit the classifications of symmetry-enriched 2D and 3D Abelian gauge theories using our results.
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@inproceedings{qing-rui2021domain,
  title={Domain Wall Decorations, Anomalies and Spectral Sequences in Bosonic Topological Phases},
  author={Qing-Rui Wang, Shang-Qiang Ning, and Meng Cheng},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220616162305199230388},
  year={2021},
}
Qing-Rui Wang, Shang-Qiang Ning, and Meng Cheng. Domain Wall Decorations, Anomalies and Spectral Sequences in Bosonic Topological Phases. 2021. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220616162305199230388.
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