在SU中的拓顺序参数的精确量化 ((N) 旋转模型,N-ality转换和ingappabilities
Hang Su1, Yuan Yao1, Akira Furusaki2,3
1Shanghai Jiao Tong University, Institute of Condensed Matter Physics, School of Physics and Astronomy, Shanghai 200240, China.
Physical review letters
|January 29, 2025
概括
一个新的拓顺序参数,扭曲运算符,精确地识别了1D旋转系统中的对称性保护拓 (SPT) 阶段. 这个参数,量化并采取单位的nth根,揭示了相位过渡,并暗示了利布-舒尔茨-马蒂斯的不可发现性条件.
科学领域:
- 凝聚物质物理学 凝聚物质物理学
- 量子多体系统是一个量子多体系统.
- 物质的拓阶段.
背景情况:
- 对称性保护的拓 (SPT) 阶段代表着由对称性特征的物质的异国情境.
- 识别和分类这些阶段,特别是在一维系统中,仍然是一个关键的挑战.
- 拓顺序参数对于区分不同的拓阶段和理解阶段过渡至关重要.
研究的目的:
- 在1D旋转系统中引入和验证U(1)-和Z_N-对称的SPT相的新拓顺序参数.
- 证明参数能够量化拓顺序,识别相位和诊断相位过渡的能力.
- 探讨这个参数对利布-舒尔茨-马蒂斯 (LSM) 隐藏性和多关键点的构造的影响.
主要方法:
- 使用非本地扭转操作员的地面状态预期值.
- 证明这个运算符在热力学极限中的量子化.
- 在通用格子转换 (N-ality转换) 下分析运算符的行为.
主要成果:
- 扭转运算符作为U(1)-和Z_N-SPT阶段的量化拓顺序参数.
- 它的值仅限于单位的nth根.
- N-ality转换连接了不同的 SPT 阶段,为阶段分类提供了新的视角.
- 该框架预测了许多Lieb-Schultz-Mattis不合适性条件,用于SU(N) 旋转.
- 开发了一种有效的方法来构建多临界相位过渡.
结论:
- 扭转操作员是1D旋转系统中SPT相的表征的强大工具.
- 这项工作在拓秩序,对称性和像LSM ingappability这样的基本约束之间建立了直接联系.
- N-ality概念为理解相位图和设计量子系统提供了一种新的方法.
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