在远程自由子链中大量的边界对应和奇点填充
Nick G Jones1,2, Ryan Thorngren3,4, Ruben Verresen5
1Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom.
Physical review letters
|June 30, 2023
概括
这项研究揭示了拓链中的远程相互作用如何创建与奇点相关的边缘模式,而不是根. 这一发现为探测量子系统中的拓绕数提供了一种新方法.
科学领域:
- 凝聚物质物理学 凝聚物质物理学
- 量子力学就是量子力学.
- 拓学材料 拓学材料
背景情况:
- 大量边界对应解释了短距离系统中的边缘模式.
- 拓链中的远程相互作用缺乏系统的研究.
研究的目的:
- 系统地研究长距离相互作用的1D自由子链中的拓不变量和边缘模式 (功率定律衰变α > 1).
- 开发一种技术来解决BDI和AIII对称类中的差距,转化不变模型.
主要方法:
- 分析由哈密尔顿合得出的复杂函数.
- 将批量拓不变量 (绕数) 与边形模式属性联系起来.
- 调查具有权力规律衰变指数α>1和α<1的模型.
主要成果:
- 长距离系统中的边缘模式与复杂函数的奇点有关,与它们与根相关的短距离系统不同.
- 边形模式的有限大小分割直接探测到拓上数.
- 结果在特定条件下扩展到具有α < 1的BDI链和无间隙链.
结论:
- 对于远距离交互的拓系统的大量边界对应的新理解.
- 边形模式的有限大小分割作为拓不变量的直接实验探测器.
- 该框架适用于各种1D拓阶段,包括那些没有间隙的边缘状态.
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