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Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries
by Sahand Seifnashri
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Sahand Seifnashri |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2308.05151v3 (pdf) |
| Date accepted: | 2024-03-18 |
| Date submitted: | 2024-03-12 14:43 |
| Submitted by: | Seifnashri, Sahand |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
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 $H^3(G,U(1)) \times H^2(G,U(1))$. 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.
Author comments upon resubmission
List of changes
Report 1:
1. Footnote 29 has been added.
2. Footnote 31 has been added.
3. We have edited Section 3.3 and added various footnotes to address the referee's point.
Report 2:
1. We only argue that we can detect the mixed anomaly between an internal symmetry and the reflection symmetry. Since the reflection symmetry is not locality-preserving (in the sense explained in Section 2), we do not know how to construct a topological defect for it.
2. A paragraph at the end of Subsection 3.1 has been added, commenting on the anomaly involving reflection.
3. We do not know how to gauge a symmetry that does not act internally, such as lattice translation. See also the new footnote 31.
Published as SciPost Phys. 16, 098 (2024)