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arXiv 1612.08682hep-th
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1+1维中的纠缠熵与边界条件

Entanglement Entropy and Boundary Conditions in 1+1 Dimensions

Ben Michel, Mark Srednicki

摘要:

在连续量子场论中计算空间区域的纠缠熵时,需要在区域的虚拟边界上设置场的边界条件。这些边界条件影响到对场的零模的处理以及它们对纠缠熵的贡献。我们在最简单的例子中探讨这个问题,即1+1维中的c=1紧玻色子共形场论。我们考虑三种不同类型的边界条件:空间诺依曼,时间诺依曼,狄利克雷。我们认为,前两个是很好的动机,并表明,他们导致相同的结果Renyi熵以及纠缠熵,包括一个常数项,对应于阿弗莱克-路德维希边界熵。最后一组边界条件的动机不太好,导致常数项的不同值。这两个值通过紧玻色子上的对偶变换联系起来。我们还验证了我们的一些结果与热核方法。

英文摘要:

Calculations of the entanglement entropy of a spatial region in continuum quantum field theory require boundary conditions on the fields at the fictitious boundary of the region. These boundary conditions impact the treatment of the zero modes of the fields and their contribution to the entanglement entropy. We explore this issue in the simplest example, the c=1 compact-boson conformal field theory in 1+1 dimensions. We consider three different types of boundary conditions: spatial Neumann, temporal Neumann, and Dirichlet. We argue that the first two are well motivated, and show that they lead to the same result for the Renyi entropies as well as the entanglement entropy, including a constant term that corresponds to the Affleck-Ludwig boundary entropy. The last set of boundary conditions is less well motivated, and leads to a different value of the constant term. The two values are related by a duality transformation on the compact boson. We also verify some of our results with heat-kernel methods.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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