共形场论的指标：纠缠熵和多点关联函数
Indicators of Conformal Field Theory: entanglement entropy and multiple-point correlators
摘要：
量子系统的纠缠熵（EE）常被用来检验共形场论（CFT）的低能描述。在这里，我们指出这不是一个可靠的指标，因为即使CFT描述不正确（只要系统是渐近尺度不变的），EE也经常显示相同的行为。我们使用SU（2）对称性的CFT给出的标度维数的约束，提供两点和四点关联函数的替代测试，显示1+1维量子自旋模型的例子。在一个临界的振幅积状态表示的价键的基础上（其中的振幅衰减的键长的幂律和波函数是所有键振幅的产品）的情况下，我们表明，即使EE表现出预期的CFT行为，有没有CFT描述这种状态。我们提供了数值测试的行为预测的临界横场伊辛链和$J$ - $Q$自旋链，共形结构是很好地理解的关联函数的CFT。这种行为在振幅乘积状态下不会再现。
英文摘要：
The entanglement entropy (EE) of quantum systems is often used as a test of low-energy descriptions by conformal field theory (CFT). Here we point out that this is not a reliable indicator, as the EE often shows the same behavior even when a CFT description is not correct (as long as the system is asymptotically scale-invariant). We use constraints on the scaling dimension given by the CFT with SU(2) symmetry to provide alternative tests with two- and four-point correlation functions, showing examples for quantum spin models in 1+1 dimensions. In the case of a critical amplitude-product state expressed in the valence-bond basis (where the amplitudes decay as a power law of the bond length and the wave function is the product of all bond amplitudes), we show that even though the EE exhibits the expected CFT behavior, there is no CFT description of this state. We provide numerical tests of the behavior predicted by CFT for the correlation functions in the critical transverse-field Ising chain and the $J$-$Q$ spin chain, where the conformal structure is well understood. That behavior is not reproduced in the amplitude-product state.
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