Braiding with Borromean Rings in (3+1)-Dimensional Spacetime.
Braiding with Borromean Rings in (3+1)-Dimensional Spacetime.
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DOI：
10.1103/physrevlett.121.061601
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发表时间：
2017-03
影响因子：
8.6
通讯作者：
A. Chan;P. Ye;S. Ryu
中科院分区：
文献类型：
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作者：
A. Chan;P. Ye;S. Ryu
当将粒子状激发缠绕在环状激发周围时，会产生著名的Aharonov-Bohm相，但在没有这种相互缠绕的情况下，我们发现了一个独特的编织相。在这封信中，我们提出了一种奇异的粒子-环状-环状编织工艺，称为Borromean环编织。在这个过程中，一个粒子绕着两个不相连的环运动，这样它的轨迹和这两个环就形成了博罗米奥环或更一般的布伦链。由于粒子轨迹不随任何环缠绕，因此产生的编织阶段与Aharonov-Bohm阶段根本不同。我们根据Milnor的三重连接数推导出编织阶段的显式表达式。我们还提出了由AAB型拓扑项组成的拓扑量子场理论，实现了编织统计。
While winding a particlelike excitation around a looplike excitation yields the celebrated Aharonov-Bohm phase, we find a distinctive braiding phase in the absence of such mutual winding. In this Letter, we propose an exotic particle-loop-loop braiding process, dubbed the Borromean rings braiding. In the process, a particle moves around two unlinked loops, such that its trajectory and the two loops form the Borromean rings or more general Brunnian links. As the particle trajectory does not wind with any of the loops, the resulting braiding phase is fundamentally different from the Aharonov-Bohm phase. We derive an explicit expression for the braiding phase in terms of the underlying Milnor's triple linking number. We also propose topological quantum field theories consisting of an AAB-type topological term which realize the braiding statistics.