Two-cylinder entanglement entropy under a twist
Two-cylinder entanglement entropy under a twist
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DOI：
10.1088/1742-5468/aa668a
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发表时间：
2016-11
期刊：
影响因子：
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通讯作者：
Xiao Chen;W. Witczak-Krempa;T. Faulkner;E. Fradkin
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文献类型：
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作者：
Xiao Chen;W. Witczak-Krempa;T. Faulkner;E. Fradkin
本文研究了2 + 1和3 + 1维时空环面上标度不变理论的von Neumann和Rényi纠缠熵。我们专注于空间的环面分为两个圆柱体的双分区，并允许扭曲的边界条件沿着不可收缩的周期。得到了相对论玻色子和狄拉克费米子共形场论（CFTs）、费米子二次带接触和z = 2 Lifshitz标度玻色子的普遍EE的各种解析和数值结果。EE的形状依赖性清楚地区分这些理论，虽然有趣的相似之处被发现在某些限制。我们还研究了EE的演变时，引入质量失谐系统从其标度不变点，通过采用重整化EE，超越了天真的减法的面积法。在某些情况下，我们发现RG流下的环面EE的非单调行为，这将其与盘的EE区分开来。
We study the von Neumann and Rényi entanglement entropy (EE) of the scale-invariant theories defined on the tori in 2 + 1 and 3 + 1 spacetime dimensions. We focus on the spatial bi-partitions of the torus into two cylinders, and allow for twisted boundary conditions along the non-contractible cycles. Various analytical and numerical results are obtained for the universal EE of the relativistic boson and Dirac fermion conformal field theories (CFTs), the fermionic quadratic band touching and the boson with z = 2 Lifshitz scaling. The shape dependence of the EE clearly distinguishes these theories, although intriguing similarities are found in certain limits. We also study the evolution of the EE when a mass is introduced to detune the system from its scale-invariant point, by employing a renormalized EE that goes beyond a naive subtraction of the area law. In certain cases we find the non-monotonic behavior of the torus EE under RG flow, which distinguishes it from the EE of a disk.