| Autor: |
Sahand Seifnashri |
| Jazyk: |
angličtina |
| Rok vydání: |
2024 |
| Předmět: |
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| Zdroj: |
SciPost Physics, Vol 16, Iss 4, p 098 (2024) |
| Druh dokumentu: |
article |
| ISSN: |
2542-4653 |
| DOI: |
10.21468/SciPostPhys.16.4.098 |
| Popis: |
We study 't Hooft anomalies of global symmetries in 1+1d lattice Hamiltonian systems. We consider anomalies in internal and lattice translation symmetries. We derive a microscopic formula for the "anomaly cocycle" using topological defects implementing twisted boundary conditions. The anomaly takes value in the cohomology group $H^3(G,U(1)) × H^2(G,U(1))$. The first factor captures the anomaly in the internal symmetry group $G$, and the second factor corresponds to a generalized Lieb-Schultz-Mattis anomaly involving $G$ and lattice translation. We present a systematic procedure to gauge internal symmetries (that may not act on-site) on the lattice. We show that the anomaly cocycle is the obstruction to gauging the internal symmetry while preserving the lattice translation symmetry. As an application, we construct anomaly-free chiral lattice gauge theories. We demonstrate a one-to-one correspondence between (locality-preserving) symmetry operators and topological defects, which is essential for the results we prove. We also discuss the generalization to fermionic theories. Finally, we construct non-invertible lattice translation symmetries by gauging internal symmetries with a Lieb-Schultz-Mattis anomaly. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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