Quantum impurity solvers for quantum materials

点击翻译按钮获取中文摘要

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.