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Lieb-Schultz-Mattis type theorem with higher-form symmetry and the quantum dimer models
- Source :
- Phys. Rev. B 99, 014402 (2019)
- Publication Year :
- 2018
-
Abstract
- The Lieb-Schultz-Mattis theorem dictates that a trivial symmetric insulator in lattice models is prohibited if lattice translation symmetry and $U(1)$ charge conservation are both preserved. In this paper, we generalize the Lieb-Schultz-Mattis theorem to systems with higher-form symmetries, which act on extended objects of dimension $n > 0$. The prototypical lattice system with higher-form symmetry is the pure abelian lattice gauge theory whose action consists only of the field strength. We first construct the higher-form generalization of the Lieb-Schultz-Mattis theorem with a proof. We then apply it to the $U(1)$ lattice gauge theory description of the quantum dimer model on bipartite lattices. Finally, using the continuum field theory description in the vicinity of the Rokhsar-Kivelson point of the quantum dimer model, we diagnose and compute the mixed 't Hooft anomaly corresponding to the higher-form Lieb-Schultz-Mattis theorem.<br />Comment: 20 pages, 4 figures
Details
- Database :
- arXiv
- Journal :
- Phys. Rev. B 99, 014402 (2019)
- Publication Type :
- Report
- Accession number :
- edsarx.1805.05367
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1103/PhysRevB.99.014402