Quantum impurity solvers for quantum materials

大多数现代技术都是围绕电子设备而建立的，而电子设备本身就是基于晶体管和固态设备。我们今天所知道的世界上的技术是几十年前发生在这个基础物理领域的科学发现的结果。今天，固态物理现在面临着一个新的挑战，理解量子材料。有了这些材料，就有可能在与人类相关的尺度上观察量子效应。这一集体努力需要时间，需要理论和实验之间的紧密合作。在理论方面，由于问题的性质，大部分工作都是针对量子材料模型中的电子的量子物理的数值模拟。在我的团队中，我们将通过开发量子材料数值模拟所需的高效开源软件库来为这一努力做出贡献。该研究计划关注对社区重要的三种不同类别的软件。1.由于变分蒙特卡罗的最新进展，现在有可能获得比以前大得多的量子模型的量子材料的激发谱。这为更精细的量子材料光谱研究打开了大门。这一进展的一个明显应用是研究铜酸盐中的假能隙。这些在高温下超导的陶瓷包含了许多悬而未决的问题。突破这种材料所能解决的模型大小的极限，似乎对解释假缝隙之谜至关重要。2.连续时间量子蒙特卡罗方法是量子材料数值模拟的参考方法。有几种算法和实现，不同的模型有不同的性能。社区的巨大努力是为了优化和开发这种形式主义的更强大的新算法。重要的是要提高这些方法的效率，以便增加有可能获得解的模型的数量，并减少计算马尔可夫链所需的时间。3.我们用来模拟量子材料的模型包含的自由度很少，否则是不可解的。它们实际上是我们试图解释的真实材料的近似值。为了得到这些近似值，我们必须应用一种严格的向下折叠技术，允许减少自由度并只保留最相关的一个。最近，利用自旋-轨道相互作用进行下行折叠已经成为可能。有了这个新的算法，现在就有可能为我们想要研究的量子材料推导出我们自己的有效模型。

Most of the modern technology is built around electronics, itself based on the transistor and solid state devices. The technologies in the world that we know today is the result of science discovery that happened many decades ago, in this fundamental field of physics. Today, solid-state physics is now faced with a new challenge, understand quantum materials. With these materials, it is possible to observe quantum effect at a scale relevant for the human. This collective effort requires time and tight collaboration between theory and experiment. On the theory side, due to the nature of the problem, much of the effort is directed towards numerical simulation of quantum physics of the electron of quantum material models. In my group, we will contribute to this effort by developing efficient open-source software libraries necessary for numerical simulation of quantum materials. This research program focuses on three different classes of software important to the community. 1. Due to recent progress in variational Monte Carlo, it is now possible to access the excitation spectrum of quantum materials for quantum models much larger than before. This opens the doors to much more elaborate spectrum studies of quantum materials. One obvious application of this progress is the investigation of the pseudogap in cuprates. These ceramics which are superconducting at high temperatures contain many unanswered questions. Pushing the limit of the size of the model that can be solved for this material seems crucial for the explanation of the pseudogap mystery. 2. Continuous-time quantum Monte Carlo is the reference method in numerical simulations of quantum materials. There are several algorithms and implementations, with different performances for different models. A great effort of the community is directed towards the optimization and the development of new more powerful algorithms of this formalism. It is important to increase the efficiency of these methods in order to increase the number of models for which it is possible to obtain solutions and reduce the time necessary for the computation of the chain of Markov. 3. The models that we seek to solve to simulate quantum materials contain very few degrees of freedom, otherwise they are not solvable. They are in fact an approximation of the real materials that we are trying to explain. To obtain these approximations, we must apply a rigorous downfolding technique which allows to reduce degrees of freedom and to keep only the most relevant one. It has recently been possible to carry downfolding with spin-orbit interaction. With this new algorithm, it is now possible to derive our own effective models for the quantum materials that we want to study.