Local moments in spin-orbit coupled systems

自旋-轨道耦合和电子关联的相互作用导致了当前固体物理研究中的各种现象。例子包括与Irate相关的广义Kitaev模型中的分馏化和相关的涌现规范理论，以及强拓扑绝缘体表面的磁性吸附原子。在这项拨款方案中，我们的目标是使用精确的辅助场量子蒙特卡罗模拟来研究这类系统的热力学和动力学性质。自旋-轨道耦合系统中电子关联的一般问题受到负号问题的影响，这使得它变得指数级困难。这里，关键的技术见解是，我们可以使用对称论点来降低负号问题的严重性。这将使我们能够获得上述系统的高温热力学和动力学性质，例如，探测单粒子光谱函数中例外点的特征。至于掺杂的Hubbard模型，我们预计我们将能够达到实验上相关的能量标度。我们的方法是基于自旋算符的费米子表示。在我们的公式中，人们可以通过给费米子附加一个均匀的味道指数来避免负号问题。该提案的另一个目标是调查这些模型，特别是解决它们是否能捕捉到无味模型的物理学方面的问题。

The interplay of spin-orbit coupling and electronic correlations leads to a variety of phenomena of current research in solid state physics. Examples include fractionalization and associated emergent gauge theories in generalized Kitaev models relevant for iridates, as well as magnetic adatoms on the surface of strong topological insulators. In this grant proposal, we aim at using exact auxiliary-field quantum Monte Carlo simulations to investigate thermodynamic and dynamical properties of such systems. The general problem of electronic correlations in spin-orbit coupled systems suffers from a negative sign problem that renders it exponentially hard. Here, the key technical insight is that we can use symmetry arguments to reduce the severity of the negative sign problem. This will allow us to access the high-temperature thermodynamic and dynamical properties of the above-mentioned systems and, for instance, probe for signatures of exceptional points in the single-particle spectral function. As for the doped Hubbard model, we foresee that we will be able to reach experimentally relevant energy scales. Our approach is based on a fermion representation of the spin operator. Within our formulation, one can avoid the negative sign problem by attaching an even flavor index to the fermions. Another goal of the proposal is to investigate these models, and in particular to address the question if they capture aspects of the physics of the flavorless ones.