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Non-invertible and higher-form symmetries in 2+1d lattice gauge theories
by Yichul Choi, Yaman Sanghavi, Shu-Heng Shao, Yunqin Zheng
Submission summary
| Authors (as registered SciPost users): | Yunqin Zheng |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202411_00032v1 (pdf) |
| Date submitted: | 2024-11-18 04:55 |
| Submitted by: | Zheng, Yunqin |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We explore exact generalized symmetries in the standard 2+1d lattice $\mathbb{Z}_2$ gauge theory coupled to the Ising model, and compare them with their continuum field theory counterparts. One model has a (non-anomalous) non-invertible symmetry, and we identify two distinct non-invertible symmetry protected topological phases. The non-invertible algebra involves a lattice condensation operator, which creates a toric code ground state from a product state. Another model has a mixed anomaly between a 1-form symmetry and an ordinary symmetry. This anomaly enforces a nontrivial transition in the phase diagram, consistent with the "Higgs=SPT" proposal. Finally, we discuss how the symmetries and anomalies in these two models are related by gauging, which is a 2+1d version of the Kennedy-Tasaki transformation.
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- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
For the first referee, we addressed all the requested changes. In particular, for question 1 and 2, we added a further explanations on page 30 and 56 respectively.
For the second referee, we added a footnote for question 1--gauging on the lattice doesn't necessarily gives a non tensor factorized Hilbert space. Rather one has the freedom to adding a flux term and only when the coefficient is infinity would give a non tensor factorized Hilbert space. For question 2, it is true that both non-invertible SPT phases reduce to the same non-trivial SPT protected by Z2^{(0)} x Z2^{(1)}. For question 3, the mixed anomaly discussed in this paper involves three symmetries (two 0-form symmetries and one 1-form symmetry). Moreover, it does not involve translation, so is different from the LSM anomaly.