Topological and Many-body Localization Phases in Spinor Bose-Hubbard Models

旋量 Bose-Hubbard 模型中的拓扑和多体定位相

基本信息

批准号：
20J20715
负责人：
YANG Hong
金额：
$ 1.98万
依托单位：
The University of Tokyo
依托单位国家：
日本
项目类别：
Grant-in-Aid for JSPS Fellows
财政年份：
2020
资助国家：
日本
起止时间：
2020-04-24 至 2023-03-31
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-20J20715/
关键词：
emergent anomaly SPT phase SPT criticality Kennedy-Tasaki duality SPT states Ultracold atoms

项目摘要

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.

以前，我们重新审视了肯尼迪 - 塔萨基二重性，并揭示了KT二元性为拓扑关键提供了“隐藏的对称性破坏”解释。我们还注意到，KT自偶性与出现的Lieb-Schultz-Mattis（LSM）异常密切相关。因此，我们专注于研究新兴的异常。使用扰动理论，我们发现临界自动划分点附近的Spin-1模型的低能量理论等同于Spin-1/2 XYZ链。这意味着，在低能理论中，完整理论的对称性Z2Y \ rtimes z2Z×Ztrn的对称性Z2Y \ rtimes Z2Z×Ztrn将其减少到Zy'x'×Zz'×Ztrn中。换句话说，在低能理论中，Z4Y \ rtimes Z2Z×ZTRN导致LSM异常，这导致没有独特的间隙基态。但是，Spin-1 Hilbert空间中的Z4Y \ rtimes Z4Z×ZTRN没有异常。换句话说，围绕自偶点的LSM异常实际上是出现的。由于Spin-1 Hilbert空间中的完整理论无异常，因此必须通过某种机制取消新兴的异常。请注意，对于间隙的对称Z2Y，在低能量理论中，非平凡的组元素（π旋转）与-1相同。这表明基态被“堆叠”在受Z2Y×ZTRN保护的张开的（弱）对称性保护拓扑（SPT）相中。正是这种SPT阶段取消了新兴的异常。我们使用现场理论来证明我们的论点。* \ rtimes是指半独立产品。