2022 Fiscal Year Annual Research Report
Topological and Many-body Localization Phases in Spinor Bose-Hubbard Models
| Project/Area Number |
20J20715
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| Research Institution | The University of Tokyo |
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Principal Investigator |
YANG Hong 東京大学, 理学系研究科, 特別研究員(PD)
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| Project Period (FY) |
2020-04-24 – 2023-03-31
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| Keywords | emergent anomaly / SPT phase |
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| Outline of Annual Research Achievements |
Previously, we revisited the Kennedy-Tasaki duality and revealed the KT duality provides a “hidden symmetry breaking” interpretation for the topological criticality. We also noticed that the KT self-duality is closely related to an emergent Lieb-Schultz-Mattis (LSM) anomaly.
However, the nature of the emergent LSM anomaly was not very clear to us before. Therefore, we focused on investigating the emergent anomaly. Using perturbation theory, we find that the low-energy theory of our spin-1 model near the critical self-dual point is equivalent to a spin-1/2 XYZ chain. This means that, near the self-dual point, the symmetry Z2y \rtimes Z2z × Ztrn of the complete theory reduces to Zy′ × Zz′ × Ztrn in the low-energy theory. In other words, in the low-energy theory, Z4y \rtimes Z2z × Ztrn leads to an LSM anomaly, which results in the absence of a unique gapped ground state. However, Z4y \rtimes Z4z × Ztrn in the spin-1 Hilbert space has no anomaly. In other words, the LSM anomaly around the self-dual point is actually emergent. Since the complete theory in the spin-1 Hilbert space is anomaly-free, the emergent anomaly has to be cancelled by some mechanism. Note that for the gapped symmetry Z2y, the nontrivial group element (π rotation) is identical to －1 in the low-energy theory. This indicates that the ground state is "stacked" on a gapped (weak) symmetry-protected topological (SPT) phase protected by Z2y × Ztrn. It is this SPT phase that cancels the emergent anomaly. We use field theory to demonstrate our argument.
* \rtimes means semi-direct product.
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| Research Progress Status |
令和4年度が最終年度であるため、記入しない。
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| Strategy for Future Research Activity |
令和4年度が最終年度であるため、記入しない。
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Research Products
(3 results)
