The continuous Multi Scale Entanglement Renormalization Anstaz (cMERA) consists of a variational method which carries out a real space renormalization scheme on the wavefunctionals of quantum field theories. In this work we calculate the entanglement entropy of the half space for a free scalar theory through a Gaussian cMERA circuit. We obtain the correct entropy written in terms of the optimized cMERA variational parameter, the local density of disentanglers. Accordingly, using the entanglement entropy production per unit scale, we study local areas in the bulk of the tensor network in terms of the differential entanglement generated along the cMERA flow. This result spurs us to establish an explicit relation between the cMERA variational parameter and the radial component of a dual AdS geometry through the Ryu-Takayanagi formula. Finally, we argue that the entanglement entropy for the half space can be written as an integral along the renormalization scale whose measure is given by the Fisher information metric of the cMERA circuit. Consequently, a straightforward relation between AdS geometry and the Fisher information metric is also established.

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关于高斯 cMERA 中的纠缠熵

连续多尺度纠缠重整化 Anstaz (cMERA) 由一种变分方法组成，该方法对量子场论的波函数进行实空间重整化方案。在这项工作中，我们通过高斯 cMERA 电路计算自由标量理论的半空间的纠缠熵。我们获得了根据优化的 cMERA 变分参数（解开器的局部密度）编写的正确熵。因此，使用每单位尺度的纠缠熵产生，我们根据沿 cMERA 流产生的微分纠缠研究了大部分张量网络中的局部区域。这一结果促使我们通过 Ryu-Takayanagi 公式在 cMERA 变分参数和双 AdS 几何的径向分量之间建立明确的关系。最后，我们认为，半空间的纠缠熵可以写为沿重整化尺度的积分，其度量由 cMERA 电路的 Fisher 信息度量给出。因此，还建立了 AdS 几何和 Fisher 信息度量之间的直接关系。