二阶拓扑绝缘体中粒子数涨落产生的纠缠
Entanglement from particle number fluctuations in a second-order topological insulator
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中文总结 AI 辅助
研究将粒子数涨落方法扩展至二维二阶拓扑绝缘体，通过四分体构造分离拓扑贡献，实现了其纠缠拓扑相变的实验可检测路径。
中文摘要 AI 辅助
高阶拓扑绝缘体是一类具有体带隙的材料，其在(d-n)维边缘上存在无能隙模式，其中n>1。尽管存在这种修正的体-边界对应关系，其二分纠缠谱仍可观测到其非平凡拓扑。受相关研究启发，这些研究表明守恒量的涨落可用于研究一维系统的拓扑，而一维系统同样具有零维边缘模式，我们将该处理方法扩展至二维二阶拓扑绝缘体，其中角态扮演着类似的角色。我们发现，在静态情形和猝灭后的时间演化中，标准二分纠缠熵和粒子数涨落均未呈现拓扑相变的显著信号，这一现象被子系统边缘的面积定律项所掩盖。通过引入子系统的四分体构造，我们证明可分离出拓扑贡献，使两个量均产生尖锐的转变峰，且通过研究远小于整个系统的子系统即可观测到该峰。由于粒子数涨落可在现有实验中实现，这些结果为高阶拓扑绝缘体中纠缠的实验检测建立了具体且可扩展的路径。
英文摘要
Higher-order topological insulators are materials with a bulk energy gap featuring gapless modes at $(d-n)$-dimensional edges, where $n > 1$. Despite this modified bulk-boundary correspondence, their nontrivial topology can nevertheless be observed through the bipartite entanglement spectrum. Inspired by works suggesting fluctuations in conserved quantities could be used to study topology in one-dimensional systems, which likewise feature zero-dimensional edge modes, we extend this treatment to a two-dimensional second-order topological insulator where corner states play an analogous role. We show that the standard bipartite entanglement entropy and particle number fluctuation lack striking signals of topological phase transitions, both in the static case and in the time evolution after a quench, obscured by an area-law term from the subsystem edges. By introducing a quadripartite construction of the subsystem, we show that it is possible to isolate the topological contributions, producing sharp transition peaks in both quantities, observable by studying subsystems much smaller than the full system. As particle number fluctuations are accessible in existing experiments, these results establish a concrete and scalable path to experimental detection of the entanglement in higher-order topological insulators.
发表机构
- Tampere University（坦佩雷大学）
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