Tensor network projection variational Monte Carlo approach to many-body quantum lattice systems

量子材料表现出莫特绝缘性、高tc超导性和巨磁阻等高度协同的多体现象。这些效应来自载流子之间的强相互作用，使这种材料对微小的外部扰动非常敏感。这个理论项目的关键科学问题是“量子材料强烈的太赫兹频率模式选择驱动是否迫使它们在比平衡条件下更高的温度下表现出超导相？”通过对这些系统进行建模，我们的目标是指导尝试优化和控制反应的实验。将这些效应扩展到室温可能对其技术应用产生潜在的巨大影响。这项工作的关键方法是实现动态稳定。所谓的卡皮察钟摆就是一个典型的例子。通过快速振动单摆的枢轴点，可以使通常不稳定的倒立状态变得稳定。类似地，最近一系列开创性的实验表明，当一个晶格以正确的方式被震动、调制或扭曲时，一个原本不稳定或隐藏的多体相可以动态稳定下来。由于两项重大的实验进展，将这一想法应用于凝聚态物质现在已经成为可能。首先是太赫兹频率下高场相干光学方法的发展，它开辟了固体中一些最重要的激发，如光学声子、超导体间隙和约瑟夫森等离子体共振，用于讯问和驱动。其次是在原子精度制造复杂过渡金属氧化物异质结构方面取得了实质性进展，这些异质结构在界面上产生了新的特性。高度选择性的强动态扭曲和静态微观调谐有望为工程和稳定量子材料中所需的秩序形式提供新的途径。在这些发展的推动下，该项目将专注于一种新的、潜在的非常强大的计算方法，称为张量网络投影，用于计算驱动的强相关系统的动态行为。这个函数包含了变分蒙特卡罗中常用的波函数的许多不同的变体。一个软件包处理所有这些在一个统一的框架将被开发。通过时变分原理对动力学的扩展将被实现。由此产生的代码将直接应用于驱动的哈伯德模型，以确定新相关性的出现，例如超导性。

Quantum materials exhibit highly cooperative many-body phenomena such as Mott- insulating behaviour, high-Tc superconductivity and colossal magnetoresistance. These effects descend from strong interactions between charge carriers and make such materials very sensitive to small external perturbations. The key scientific question in this theory project is 'does intense THz frequency mode-selective driving of quantum materials coerce them into exhibiting a superconducting phase at higher temperatures than it would under equilibrium conditions?'. By modelling these systems our aim is to guide experiments trying to optimise and control the responses. Extending these effects to room temperature could have a potentially enormous impact on their technological applications. This key approach of this work is to implement dynamical stabilisation. The so-called Kapitza pendulum is an archetypal example. By rapidly vibrating the pivot point of a simple pendulum the usually unstable inverted state can be made stable. Analogously, a series of ground- breaking experiments have recently shown that when a crystal lattice is shaken, modulated or distorted in the right way, then an otherwise unstable or hidden many-body phase can be dynamically stabilised. Application of this idea to condensed matter has now become possible because of two significant experimental advances. The first is the development of high-field coherent optical methods at THz frequencies, which has opened up some of the most important excitations in solids, like optical phonons, superconductor gaps, and Josephson plasma resonances, for interrogation and driving. The second is the substantial progress in fabricating, with atomic precision, complex transition metal oxide heterostructures that induce novel properties at interfaces. Together highly selective strong dynamical distortions and static microscopic tuning promise to deliver new pathways for engineering and stabilising desired forms of order in quantum materials. Motivated by these developments this project will focus on a new and potentially very powerful computational approach, called tensor network projection, for computing the dynamical behaviour of driven strongly-correlated systems. This ansatz contains within it many different variants of commonly used wave functions in variational Monte Carlo. A software package handling all of these in a unified framework will be developed. Extensions to dynamics via the time-dependent variational principle will be implemented. The resulting codes will then be applied directly to the driven Hubbard model to ascertain the emergence of novel correlations, such as superconductivity.