Tensor networks for quantum matter, quantum fields, and holography

用于量子物质、量子场和全息术的张量网络

• 批准号: RGPIN-2017-04209
• 负责人: VidalBonafont, Guifre
• 金额: $ 5.1万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=667775
• 关键词: Tensor; networks; quantum; matter; fields

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. ***This Discovery Grant will advance and further develop the tensor network formalism in three important directions. Firstly, for quantum matter on the lattice (e.g. a lattice model of quantum spins for antiferromagnetic materials). Tensor networks were originally developed for lattice models of quantum matter, which are simplified models believed to capture the essential features of a many-body system. Secondly, for quantum fields directly in the continuum. Tensor networks for continuous systems are currently under construction, and could revolutionize how we think about and compute with strongly interacting quantum fields. Thirdly, tensor networks will be investigated as a realization of the holographic principle, which relates a theory of quantum gravity with a quantum field theory.***Thus, through a bold, multi-disciplinary research program in theoretical physics, this Discovery Grant aims to further strengthening Canada's leading role and international visibility in the areas of condensed matter, quantum information, computational physics, and high energy physics. The Grant will also contribute significantly to the training of highly qualified personnel, which will be exposed to fore-front research by leading experts in one of the world's most prestigious institutes for theoretical physics. ***********

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。***这项发现基金将在三个重要方向上推进和进一步发展张量网络形式主义。首先，对于晶格上的量子物质（例如反铁磁材料的量子自旋的晶格模型）。张量网络最初是为量子物质的晶格模型开发的，这是一种简化的模型，被认为可以捕捉到多体系统的基本特征。第二，对于直接处于连续介质中的量子场。连续系统的张量网络目前正在建设中，它可以彻底改变我们对强相互作用量子场的思考和计算方式。第三，张量网络将作为全息原理的实现进行研究，全息原理将量子引力理论与量子场论联系起来。因此，通过一项大胆的、多学科的理论物理研究计划，这项发现基金旨在进一步加强加拿大在凝聚态物质、量子信息、计算物理和高能物理领域的领导作用和国际知名度。该基金还将为培养高素质人才做出重大贡献，这些人才将接触到世界上最负盛名的理论物理研究所之一的顶尖专家的前沿研究。***********