Numerical simulation of topological and exotic states of quantum matter (C01)

电子相关可以动态地产生具有与底层自由电子系统非常不同性质的物质的新状态。在这项拨款提案中，我们将把重点放在相互作用费米子的标准模型上，在这些模型中，涌现的现象具有拓扑性质和/或导致奇异的相位和相变。我们将考虑重费米子系统，两个空间维度的电子-声子模型，以及不同维度的单狄拉克锥系统。我们的研究建立在算法进步的基础上，使我们能够使用无负号和无近似的量子蒙特卡罗方法解决不断增长的模型。

Electronic correlations can dynamically generate novel states of matter with very different properties than the underlying free-electron system. In this grant proposal, we will place emphasis on standard models of interacting fermions where the emergent phenomena are of a topological nature and/or lead to exotic phases and phase transitions. We will consider heavy-fermion systems, electron-phonon models in two spatial dimensions, and systems with a single Dirac cone in various dimensions. Our research builds on algorithmic advances that enable us to tackle an ever-growing range of models with negative-sign-free and approximation-free quantum Monte Carlo methods.