Tensor network approaches to quantum many-body phenomena

量子力学为我们提供了微观物体在原子和亚原子尺度上行为的基本规则。然而，当我们把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共同行为。例如，尽管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，并相信我们有一个关于它们如何相互作用的准确微观模型，但我们还无法从这个微观模型推导出超导的出现。张量网络是一种新的描述量子多体系统集体态的方法，它建立在我们对量子纠缠理解的最新进展的基础上。我的研究计划是基于进一步发展量子多体系统张量网络的形式，无论是在离散的(晶格模型，如反铁磁材料的量子自旋模型)还是在连续统(用于粒子物理的量子场论)中。我还将把这些新技术应用于几个科学技术领域的一系列悬而未决的问题，其中量子多体现象发挥着突出的作用，首先是凝聚态物质和高能物理，但也包括量子化学、纳米技术、量子计算和弦理论。

Quantum Mechanics provides us with the basic rules of how microscopic objects behave at the atomic and subatomic scales. However, when we put 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. My research program is based on further developing the formalism of tensor networks for quantum many-body systems both in the discrete (lattice models, such as models of quantum spins for antiferromagnetic materials) and in the continuum (quantum field theories, used in particle physics). I will also apply these novel techniques to a range of open problems in several areas of science and technology where quantum many-body phenomena play a prominent role, foremost condensed matter and high energy physics, but also quantum chemistry, nanotechnology, quantum computation and string theory.