Vasseur Romain, Jacobsen Jesper Lykke, Saleur Hubert
Department of Physics, University of California, Berkeley, Berkeley, California 94720, USA and Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
LPTENS, 24 rue Lhomond, 75231 Paris, France and Université Pierre et Marie Curie, 4 place Jussieu, 75252 Paris, France.
Phys Rev Lett. 2014 Mar 14;112(10):106601. doi: 10.1103/PhysRevLett.112.106601. Epub 2014 Mar 10.
We consider the entanglement between two one-dimensional quantum wires (Luttinger liquids) coupled by tunneling through a quantum impurity. The physics of the system involves a crossover between weak and strong coupling regimes characterized by an energy scale TB, and methods of conformal field theory therefore cannot be applied. The evolution of the entanglement in this crossover has led to many numerical studies, but has remained little understood, analytically or even qualitatively. We argue in this Letter that the correct universal scaling form of the entanglement entropy S (for an arbitrary interval of length L containing the impurity) is ∂S/∂ ln L=f(LTB). In the special case where the coupling to the impurity can be refermionized, we show how the universal function f(LTB) can be obtained analytically using recent results on form factors of twist fields and a defect massless-scattering formalism. Our results are carefully checked against numerical simulations.
我们考虑通过量子杂质隧穿耦合的两条一维量子线（卢廷格液体）之间的纠缠。该系统的物理过程涉及由能量尺度(T_B)表征的弱耦合和强耦合区域之间的交叉，因此共形场论方法无法应用。这种交叉中纠缠的演化引发了许多数值研究，但在解析上甚至定性上仍知之甚少。我们在这封信中指出，纠缠熵(S)（对于包含杂质的任意长度(L)的区间）的正确普适标度形式为(\frac{\partial S}{\partial \ln L}=f(LT_B))。在与杂质的耦合可以重费米子化的特殊情况下，我们展示了如何利用最近关于扭场形状因子的结果和缺陷无质量散射形式理论解析地得到普适函数(f(LT_B))。我们的结果与数值模拟进行了仔细核对。
