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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.

在此之前，我们重新审视了Kardy-Tasaki对偶，并揭示了KT对偶为拓扑临界性提供了一个“隐藏对称破缺”的解释。我们还注意到KT自对偶与突现的Leb-Schultz-Mattis（LSM）反常密切相关，然而，突现的LSM反常的性质我们以前并不十分清楚。因此，我们专注于调查紧急异常。利用微扰理论，我们发现自旋为1的模型在临界自对偶点附近的低能理论等价于自旋为1/2的XYZ链。这意味着，在自对偶点附近，完全理论的对称性Z2 y\r × Z2 z × Ztrn在低能理论中简化为Zy′ × Zz′ × Ztrn。换句话说，在低能理论中，Z4 y\r × Z2 z × Ztrn导致LSM异常，这导致缺乏唯一的带隙基态。然而，自旋为1的希尔伯特空间中的Z4 y\r × Z4 z × Ztrn没有反常。换句话说，自对偶点周围的LSM异常实际上是突现的。由于自旋为1的希尔伯特空间中的完备理论是无反常的，因此必须通过某种机制消除突现反常。注意，对于带隙对称性Z2 y，非平凡群元素（π旋转）等同于低能理论中的-1。这表明基态被“堆叠”在由Z2 y × Ztrn保护的带隙（弱）拓扑保护（SPT）相上。正是这个SPT阶段取消了紧急异常。我们用场论来证明我们的论点。\r times表示半直积。