Emerging correlations from strong driving: a tensor network projection variational Monte Carlo approach to 2D quantum lattice systems

我们拥有的大部分技术都是基于开发特殊材料，如半导体。下一场革命可能来自所谓的量子材料。然而，虽然它们的行为有可能非常有用，但理解和控制也很复杂。从这项研究中获得的见解将有助于确定用光控制量子材料的可行性，以及在未来纳米器件中可能利用动态非平衡特性。用光控制材料是有趣的，因为众所周知，驱动系统可以表现出静止时看不到的行为。这里有两个简单的例子。第一个是所谓的卡皮查摆。这是一个正常的摆，其支点经历快速但振幅小的垂直振荡。这个摆的惊人之处在于，通常对重力不稳定的倒立位置通过周期性驱动而动态稳定。第二个是一个旋转鞍上的球。当鞍座静止时，球不能稳定地定位在拐点处。然而，如果鞍座旋转超过某个阈值角速度，则球可以在由鞍座扫出的时间平均碗中平衡。同样的想法也适用于材料等多体系统，研究它们的行为变得越来越重要。一类重要的多体系统是那些由于其成分之间的相互作用而表现出强相关性的系统。日常生活中充满了这样的系统。例如，由于许多车辆的组合以及它们之间的强烈排斥以避免占用同一条道路，因此沿着沿着形成交通堵塞。然而，尽管蚂蚁们面临着非常相似的限制，但排成一行的蚂蚁却从来没有遇到过这样的交通堵塞，因为它们不会互相超过。这两个例子表明，相互作用的精确微观性质的细微差异可能导致定性不同的宏观性质。描述这样的关联性对相互作用系统的理论研究提出了重大挑战，而量子系统的情况也是如此。在量子的情况下，强相互作用导致了凝聚态物质中一些最不容易理解的现象，如高Tc超导，挫折和拓扑相，如分数量子霍尔物理。这些效应只在低温下出现，并且通常出现在具有主导二维特征的材料中。由于量子材料具有功能特性，因此有一项重大的研究工作是在更高的温度下稳定和优化它们，以用于未来的技术应用。最近的一种方法是周期性地驱动多体量子系统，以“动态稳定”宏观量子效应，使其超出平衡状态。高场太赫兹产生技术的惊人进步使这个问题变得更加引人注目。这允许选择性地驱动真实的固体的低能量激发，如振动，使得晶格能够以受控的方式被摇动、调制或扭曲。这在驱动系统和多体物理学之间创造了一个令人兴奋的界面，吸引了全球大量的研究人员。阻碍在工程材料中使用周期性驱动的一个关键问题是加热，这可能会消除所需的效果。这个项目在最重要的哈伯德模型（Hubbard model）的背景下研究这个问题，哈伯德模型捕捉了强相关的基本物理学。目前的数值方法很难对这个问题给出一个结论性的答案。该项目的一个独特之处将是开发一种结合蒙特卡罗和张量网络的方法，这种方法可能足够丰富，可以准确地描述驱动哈伯德模型的动力学行为。由此产生的高性能软件将在计算机上可用。

Much of the technology we have is based on exploiting special materials like semiconductors. The next revolution is likely to emerge from so-called quantum materials. However, while their behaviour has the potential to be extremely useful, it is also complex to understand and control. Insights gained from this research will help determine the viability of controlling quantum materials with light and the possible exploitation of dynamical non-equilibrium properties in future nano-devices. Controlling materials with light is interesting because it is well known that driven systems can exhibit behaviour not seen when stationary. There are two simple examples of this. The first is a so-called Kapitza pendulum. This is a normal pendulum whose pivot point undergoes vertical oscillations that are rapid but small in amplitude. What is striking about this pendulum is that the inverted position, normally unstable to gravity, is dynamically stabilised by the periodic driving. The second is a ball on a rotating saddle. The ball cannot be stably positioned at the inflection point when the saddle is stationary. However, if the saddle is rotated above some threshold angular velocity then the ball can be balanced in the time-averaged bowl swept out by the saddle. The same ideas apply to many-body systems like materials and it is becoming increasingly relevant to study their behaviour.An important class of many-body systems are those that exhibit strong correlations due to interactions between their constituents. The everyday world is full of such systems. For example traffic jams form along roads due to a combination of many vehicles and a strong repulsion between them to avoid occupying the same piece of road. However, ants marching in a line never suffer from such traffic jams despite facing very similar restrictions because they don't overtake one another. These two examples demonstrate how subtle differences in the precise microscopic nature of interactions may lead to qualitatively different macroscopic properties. Describing such correlations poses major challenges for the theoretical study of interacting systems, and no more so than for the case of quantum systems. In the quantum case strong interactions lead to some of the least well-understood phenomena of condensed matter, like high-Tc superconductivity, frustration, and topological phases such as fractional quantum Hall physics. These effects only appear at low temperatures and typically in materials with a dominant two-dimensional character.Since quantum materials exhibit functional properties there is a major research effort to stabilise and optimise them at higher temperatures for future technological applications. A recent approach to this is to periodically drive a many-body quantum system to "dynamically stabilise" macroscopic quantum effects beyond where they occur in equilibrium. The question is made even more compelling by spectacular advances in high-field THz generation technology. This allows selective driving of low-energy excitations of real solids, like vibrations, enabling a crystal lattice to be shaken, modulated or distorted in controlled ways. This has created an exciting interface between driven systems and many-body physics engaging a large body of researchers worldwide.A crucial issue hampering the use of periodic driving in engineering materials is heating that might wash out the desired effects. This project examines this problem within the context of one of the most important model Hamiltonians, the Hubbard model, which captures the essential physics of strong correlations. Current numerical methods struggle to give a conclusive answer to this issue. A unique feature of this project will be the development of a combined Monte Carlo and tensor network approach potentially rich enough to accurately describe the dynamical behaviour of the driven Hubbard model. The resulting high performance software will be publically available.