AI 中文总结
研究确定临界系统矩阵乘积态近似实际微扰的问题，开发稀疏线性求解器计算二维张量网络导数，解决开放问题，且算法能用于投影纠缠对态变分优化，避免传统方法不稳定性。
AI 中文摘要
有限纠缠标度的概念是张量网络体系的支柱之一。本文解决了确定临界系统矩阵乘积态近似所引起的实际微扰这一开放问题，证明其与共形场论预测的不同。为此，开发了一种稀疏线性求解器，以隐式方式计算二维张量网络关于其定义参数的前向和后向导数。该算法可用于投影纠缠对态的变分优化，避免传统自动微分方法的不稳定性。
英文摘要
The concept of finite entanglement scaling forms one of the pillars on which the tensor network ecosystem is built. In this paper, we resolve the open problem of determining the actual perturbations induced by matrix product state approximations of critical systems, and we demonstrate that these can be quite different than the ones predicted by conformal field theory. To that aim, we develop a sparse linear solver to calculate the forward and backward derivatives of 2-dimensional tensor networks with respect to their defining parameters in an implicit way. This algorithm is of independent interest as it provides a primitive for the variational optimization of projected entangled pair states that circumvents the instabilities plaguing traditional automatic differentiation methods.
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