General Lieb?Schultz?Mattis Type Theorems for Quantum Spin Chains
General Lieb?Schultz?Mattis Type Theorems for Quantum Spin Chains
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量子自旋链的一般李布·舒尔茨·马蒂斯型定理
DOI：
10.1007/s00220-021-04116-9
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发表时间：
2021
影响因子：
2.4
通讯作者：
Tasaki Hal
中科院分区：
文献类型：
--
作者：
Ogata Yoshiko;Tachikawa Yuji;Tasaki Hal
我们发展了一个一般的算子代数方法，它侧重于对称群的投影表示，以证明Lieb-Schultz-Mattis型定理，即，对于具有在位对称性的量子自旋链，排除存在唯一的带隙基态（或者更一般地说，纯分裂态）的不可行定理。我们首先证明了平移不变自旋链的一个定理，它统一和扩展了两个作者证明的两个定理（绪方和田崎，通讯。372951 -962，（2019）https：//doi.org/10.1007/s00220-019-03343-5）。然后，我们证明了一个Lieb-Schultz-Mattis型定理的自旋链是不变的反射下的起源，不一定平移不变。
We develop a general operator algebraic method which focuses on projective representations of symmetry group for proving Lieb–Schultz–Mattis type theorems, i.e., no-go theorems that rule out the existence of a unique gapped ground state (or, more generally, a pure split state), for quantum spin chains with on-site symmetry. We first prove a theorem for translation invariant spin chains that unifies and extends two theorems proved by two of the authors (Ogata and Tasaki, Commun. Math. Phys.372951–962, (2019) https://doi.org/10.1007/s00220-019-03343-5). We then prove a Lieb–Schultz–Mattis type theorem for spin chains that are invariant under the reflection about the origin and not necessarily translation invariant.