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

多体量子晶格系统的张量网络投影变分蒙特卡罗方法

• 批准号: 1941898
• 金额: --
• 依托单位: University of Bristol
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2017
• 资助国家: 英国
• 起止时间: 2017 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-1941898
• 关键词: Tensor; network; projection; variational; Monte

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.

量子材料表现出高度合作的多体现象，如莫特绝缘行为，高Tc超导和巨磁阻。这些效应源于电荷载体之间的强烈相互作用，使此类材料对微小的外部扰动非常敏感。这个理论项目中的关键科学问题是“量子材料的强烈太赫兹频率模式选择驱动是否会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，我们的目标是指导实验，试图优化和控制响应。将这些效应扩展到室温可能会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。所谓的卡皮查摆就是一个典型的例子。通过快速振动单摆的支点，通常不稳定的倒立状态可以变得稳定。类似地，最近一系列突破性的实验表明，当晶格以正确的方式振动、调制或扭曲时，原本不稳定或隐藏的多体相可以动态稳定。由于两个重要的实验进展，将这一想法应用于凝聚态物质现在已经成为可能。第一个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，用于询问和驱动。第二个是在制造方面取得的实质性进展，原子精度，复杂的过渡金属氧化物异质结构，诱导界面处的新特性。结合高度选择性的强动力学扭曲和静态微观调谐，有望为量子材料中的工程和稳定所需形式的秩序提供新的途径。受这些发展的推动，该项目将专注于一种新的和潜在的非常强大的计算方法，称为张量网络投影，用于计算驱动强相关系统的动力学行为。这个模型包含了在变分蒙特卡罗中常用的波函数的许多不同的变体。将开发一个软件包，在一个统一的框架内处理所有这些问题。通过时间相关的变分原理的动态扩展将被实施。由此产生的代码将直接应用于驱动哈伯德模型，以确定新的相关性的出现，如超导性。