Computational Quantum Materials

在过去的几十年里，所谓的强相关性问题一直是密集研究的焦点。虽然描述单个量子粒子通常是可能的，但如果几个粒子相互作用并不得不将它们的行为关联起来，那么预测它们的行为就困难得多，特别是如果这种相互作用导致沮丧的话。最终，这种关联效应可以主宰物理学，我们谈论的是强关联系统。存在这样一类材料，其中这种关联效应是至关重要的，并导致具有令人惊讶的性质的新的和奇异的相的存在。很快，以下问题就出现了。这些相是什么，我们如何描述它们的性质并理解相关的量子相变？如果激发是在远离基态的地方产生的，这些激发是什么，如何描述它们，如果一种材料是在激发状态下制备的，它将如何达到平衡？如果我们暂时忽略相互作用，转而考虑无序的影响，对于许多材料来说，无序是固有的或很容易引入的，那么人们可能会认为玻璃相会出现，而且这种相已经被证明出现在许多模型中。因此，很自然地会问一个非常困难的问题：当无序和强相关性都存在时，会发生什么？单个杂质是如何与系统其余部分的多体状态纠缠的，会出现哪些新的相？在许多情况下，回答所有这些问题的唯一方法是使用最先进的计算方法，本提案旨在做到这一点。这些新相和新材料的微妙之处需要新的工具来描述和数值研究它们。幸运的是，量子信息领域的概念和量子光学的想法导致了凝聚态领域许多令人兴奋的新发展。这些进展中最主要的是新的先进的数值方法，这些方法使我们能够表征量子材料中的这种新相，并检测以前没有注意到的微妙的量子相变。本提案旨在将这些新的计算技术用于量子材料的研究，目的是回答上述提出的问题。这将带来对量子材料的关键新见解，并显著提高我们执行高级计算模拟的能力。

The so-called strong correlation problem has been the focus of intense research over the last decades. While it is often possible to describe a single quantum particle it is much more difficult to predict the behavior of several particles if these interact and have to correlate their behavior in particular if the interaction gives rise to frustration. Eventually, such correlation effects can dominate the physics and we talk about strongly correlated systems. A class of materials exists for which such correlation effects are crucial and leads to the presence of novel and exotic phases with surprising properties. Immediately, the following questions arise. What are these phases and how can we characterize their properties and understand the associated quantum phase transitions ? If excitations are created away from the ground-state what are these excitations and how can be described them and if a material is prepared in an excited state how will it reach equilibrium ? If we for a moment neglect interactions and instead consider the effect of disorder, which for many materials is inherently present or can easily be introduced, then one might expect glassy phases to appear and such phases have been shown to occur in a number of models. It is then natural to ask the very difficult question: What happens when both disorder and strong correlations are present ? How does a single impurity become entangled with the many-body state of the rest of the system and what new phases can appear ? In many cases the only way to answer all of these questions is through the use of state of the art computational method and this proposal aims to do that. The subtleness of these new phases and materials require new tools for describing and for studying them numerically. Fortunately, concepts from the field of quantum information and ideas from quantum optics have led to many exciting new developments in the field of condensed matter. Chief among these developments are new advanced numerical methods that allows us to characterize such new phases in quantum materials and detect the subtle quantum phase transitions that had previously gone un-noticed. The present proposal aims to use these new computational techniques for the study of quantum materials with the goal of answering the questions raised above. This will lead to key new insights of quantum materials and significantly advance our ability to perform advanced computational simulations.