Reorganization of Edge Modes: Quantum Phase Transitions and Textures

尽管早期尝试描述量子霍尔系统边缘的量子相变，但我们提出的项目开辟了新的视野。该提案代表了两个主要目标：1。一方面，在边缘上自然发生（或诱导）量子相变（qpt）的新类别（例如，自旋开关转换；自发时间反转对称破缺）。为什么这很重要？除了发现和分析拓扑系统中新类型相变的基本物理重要性之外，后者对通过这种设置的电荷和自旋输运具有重要意义。此外，时间反转对称性的自发击穿可能发生在其他时间反转不变系统中，这一事实可能意味着应该重新关注量子计算所必需的“拓扑保护”（例如，在TRI拓扑绝缘体中）。2. 另一方面，人工设计的手性和螺旋边的物理学。heblum小组最近的实验（第一批刚刚发布，见Y. Ronen et al., arXiv:1709.03976(2017)）预示着一个新时代的到来：人们可以在整数和分数体系中随意设计复合边缘（由多个手性模式组成）。为什么这很重要？然后可以控制边缘手性模式之间的相互作用和隧道，以及每个模式的自旋内容，极大地丰富了相关一维问题的研究范围。人们可能会考虑控制干涉仪的想法，克服任意子干涉测量的逃避物理。此外，按需生产各种（整数和分数）拓扑绝缘体的道路现在似乎是开放的。解决这些问题所需的工具包括场论方法、对称破缺模式分析、非平衡量子系统理论。由于他们之前在量子霍尔和拓扑绝缘体物理领域的经验，两位pi非常熟悉这些工具，并取得了有影响力的成就，包括：非平衡玻色子化的发展和应用；预测拓扑绝缘体中自发时间反转对称性破缺，首次通过马赫-曾德干涉法预测分数统计量；首次分析了由任意子物理引起的分数阶Aharonov-Bohm振荡，包括法布里-珀罗干涉仪中相互作用效应的分析。这两个pi有着悠久的合作历史，并发表了一些共同的出版物。他们的合作包括多次互访和交换年轻团队成员。

Notwithstanding earlier attempts at describing quantum phase transitions on the edge of quantum Hall systems, our proposed project opens new horizons. The proposal represents two main thrusts: 1. On the one hand, novel classes of naturally occurring (or induced) quantum phase transitions (QPTs) on the edge (e.g., spin switching transitions; spontaneous time reversal symmetry breaking). Why is this important? Beyond the basic physics importance of discovering and analyzing new classes of phase transitions in topological systems, the latter have implications on charge and spin transport through such setups. Moreover, the fact that spontaneous breakdown of time reversal symmetry may take place in otherwise time reversal invariant systems, may imply that renewed attention should be given to “topological protection” (e.g., in TRI topological insulators), necessary for quantum computation. 2. On the other hand, the physics of artificially engineered chiral and helical edges. Very recent experiments by the Heiblum group (the first batch of which has just been posted, see Y. Ronen et al., arXiv:1709.03976 (2017)), herald a new era: one can design a composite edge (made up of multiple chiral modes) both in the integer and the fractional regimes at will. Why is this important? One may then control the interaction and tunneling between edge chiral modes, and the spin content of each mode, tremendously enriching the scope of relevant one-dimensional problems to be studied. One can possibly entertain the idea of controlled interferometers, overcoming the evading physics of anyonic interferometry. Furthermore, the road to an on-demand large variety of (integer and fractional) topological insulators now seems to be open. The tools needed to attack these problems include field theoretical methods, analysis of symmetry breaking patterns, the theory of non-equilibrium quantum systems. The two PIs are well acquainted with these tools due to their previous experience in the fields of quantum Hall and topological insulator physics, with impactful achievements that include: the development and applications of non-equilibrium bosonization; the prediction of spontaneous time-reversal symmetry breaking in topological insulators, the first predictions of fractional statistics through Mach-Zender interferometry; the first analysis of fractional Aharonov-Bohm oscillations due to anyonic physics, including the analysis of interaction effects in Fabry-Perot interferometers. The two PIs have a long history of collaboration that results in several common publications. Their collaboration has included numerous mutual visits, and exchange of young members of their teams.