Two dimensional gauge invariant tensor networks

尽管是我们对自然的理解的核心，但对处于和处于平衡状态的相关量子多体系统的研究仍然是量子物理学的一大挑战。在许多情况下，可用的解析方法和数值方法都有很大的局限性，只能描述感兴趣的物理的一个近似版本。在过去的十年中，张量网络方法开辟了新的可能性，现在是模拟一维相关量子动力学的标准工具。然而，二维多体量子系统动力学在大多数有趣的环境中仍然无法进行数值模拟。提供新颖的数值算法来解决这一挑战，将为量子技术、量子场理论、凝聚态物质和临界现象等不同的物理领域遮光。基于我介绍的一维系统的一些最新发展-晶格规范张量网络，最优控制理论和分层张量网络-以及高性能计算，本项目旨在采取前所未有的步骤：-二维晶格规范理论的数值模拟方法的发展；-研究目前阻碍量子技术发展的开放问题，以及我们对受挫自旋系统（量子二聚体模型、价键态）、拓扑模型和描述量子电动力学和色动力学方面的晶格上的高能二维模型的理解。该项目将为探索未知领域铺平道路，对相关多体量子物理的基本方面产生影响。该项目的结果也将作为第一代量子模拟器的高度重要的基准，并且-由于其实现的极端复杂性-用于验证。

The study of correlated quantum many-body systems in and out of equilibrium - despite being at the heart of our understanding of Nature - remains one of the big challenge of quantum physics. Analytical and numerical methods available are in many cases strongly limited and allow to describe only an approximated version of the physics of interests. In the lat decade, tensor network methods opened new possibilities and are now a standard tool to simulate one-dimensional correlated quantum dynamics. However, two-dimensional many-body quantum system dynamics are still out of reach of numerical simulations in most interesting settings. Providing novel numerical algorithms to solve this challenge, would shade light into different fields of physics as quantum technologies, quantum field theories, condensed matter and critical phenomena. Building on some recent developments I have introduced for one-dimensional systems -lattice gauge tensor networks, optimal control theory, and hierarchical tensor networks- together with high- performance computing, this project aims to take unprecedented steps towards: - the development of numerical simulations methods for two-dimensional lattice gauge theories; - the study of open problems that nowadays hinder the development of quantum technologies and our understanding of the properties of frustrated spin systems (quantum dimer models, valence bond states), topological models, and high-energy two dimensional models on a lattice describing aspects of quantum electrodynamics and chromodynamics. This project will pave the way to investigations in unchartered territory with impact on fundamental aspects of correlated many-body quantum physics. The results of this project will serve also as highly non trivial benchmarks for the first generation of quantum simulators, and - due to the extreme complexity of their implementation - for their verification.