Tensor networks for quantum matter, quantum fields, and holography

量子力学为我们提供了微观物体在原子和亚原子尺度上的行为的基本规则。然而，当我们将许多这样的量子物体放在一起时，我们无法从理论上预测它们的集体行为。例如，即使我们知道一类高温超导材料（称为铜酸盐）中的电子遵守量子力学定律，并且相信我们有一个精确的微观模型来解释它们如何相互作用，我们还不能从微观模型中推导出超导性的出现。张量网络是一种表示量子多体系统集体状态的新方法，基于我们对量子纠缠的最新理解。

Quantum Mechanics provides us with the basic rules of how microscopic objects behave at the atomic and subatomic scales. However, when we place many such quantum objects together, we are not capable of theoretically predicting how they will behave collectively. For instance, even though we know that the electrons in a class of high-temperature superconducting materials (called cuprates) obey the laws of Quantum Mechanics, and believe that we have an accurate microscopic model for how they interact with each other, we have not yet been able to derive the emergence of superconductivity from that microscopic model. Tensor networks are a new way of representing the collective state of quantum many-body systems, based on recent improvements in our understanding of quantum entanglement.