论文标题
量子旋转链的一般Lieb-Schultz-Mattis类型定理
General Lieb-Schultz-Mattis type theorems for quantum spin chains
论文作者
论文摘要
我们开发了一种通用操作员代数方法，该方法的重点是对称群的投影表示，用于证明Lieb-Schultz-Mattis型定理，即无需定理，这些定理排除了存在独特的间隙基地状态（或更一般而言，纯粹的分式状态），用于具有量子旋转链，用于与现场对称的量子旋转链。我们首先证明了对翻译不变链链的定理，该定理统一并扩展了[OT1]中的两个作者证明的两个定理。然后，我们证明了一个lieb-schultz-mattis型定理，用于旋转链，这些链条在反思下不变，而不一定是不变的。
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 in [OT1]. 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.
