Evolution operators in conformal field theories and conformal mappings: Entanglement Hamiltonian, the sine-square deformation, and others
Evolution operators in conformal field theories and conformal mappings: Entanglement Hamiltonian, the sine-square deformation, and others
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共形场论和共形映射中的演化算子：纠缠哈密顿量、正弦平方变形等
DOI：
10.1103/physrevb.93.235119
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发表时间：
2016
影响因子：
3.7
通讯作者：
A. Ludwig
中科院分区：
文献类型：
--
作者：
X. Wen;S. Ryu;A. Ludwig
利用共形映射，我们构造了（1+1）维共形场论中的各种时间演化算子，其形式为$\int dx\，f（x）\mathcal{H}（x）$，其中$\mathcal {H}（x）$是共形场论的哈密顿密度，$f（x）$是包络函数.这种变形的演化算子的例子包括纠缠哈密顿量，和所谓的正弦平方变形的CFT。在我们的建设中，频谱和（有限大小）标度的水平间距的变形演化算子是确切地知道。基于我们的构造，我们还提出了正弦平方变形的正则化版本，与原始的正弦平方变形相比，它具有定义在有限周长L$的空间圆上的CFT的谱，并且一旦适当地调整圆的周长和正则化参数，其水平间距缩放为1/L^2$。
By making use of conformal mapping, we construct various time-evolution operators in (1+1) dimensional conformal field theories (CFTs), which take the form $\int dx\, f(x) \mathcal{H}(x)$, where $\mathcal{H}(x)$ is the Hamiltonian density of the CFT, and $f(x)$ is an envelope function. Examples of such deformed evolution operators include the entanglement Hamiltonian, and the so-called sine-square deformation of the CFT. Within our construction, the spectrum and the (finite-size) scaling of the level spacing of the deformed evolution operator are known exactly. Based on our construction, we also propose a regularized version of the sine-square deformation, which, in contrast to the original sine-square deformation, has the spectrum of the CFT defined on a spatial circle of finite circumference $L$, and for which the level spacing scales as $1/L^2$, once the circumference of the circle and the regularization parameter are suitably adjusted.