Local moments in spin-orbit coupled systems

自旋轨道耦合和电子相关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iridates相关的广义Kitaev模型中的分块化和相关的紧急规范理论，以及强拓扑绝缘体表面的磁性附着原子。在这项拨款提案中，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些系统的热力学和动力学特性。自旋轨道耦合系统中电子相关的一般问题存在一个负号问题，使其具有指数难度。这里，关键的技术见解是，我们可以使用对称参数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特性，例如，探测单粒子谱函数中异常点的特征。对于掺杂的Hubbard模型，我们预见我们将能够达到实验相关的能量尺度。我们的方法是基于自旋算子的费米子表示。在我们的公式中，我们可以通过给费米子附加一个偶味指数来避免负号问题。该提案的另一个目标是研究这些模型，特别是解决它们是否捕获了无味的物理方面的问题。

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.