Quantum Monte Carlo studies of spin liquids and correlation induced effects in topological band insulators

固态物理学中的拓扑学依赖于这样一种思想，即物质的状态可以由全局量来表征，而不是由封装对称破缺的局域有序参数来表征。在这项拨款提案中，我们将集中研究拓扑起主导作用的量子多体现象。最近在蜂窝晶格上的Hubbard模型中观察到的有间隙的量子自旋液体相[1]需要进行表征。它可以用一个拓扑序参数来描述吗？或者它是一种变相的带状绝缘体？为了解决这个问题，我们将开发数值方法来探索拓扑简并性。我们还将修改模型哈密顿量，以尝试将量子自旋液体相绝热地继续到已知的带绝缘态。哈密顿量的一种这样的修改是包括自旋-轨道耦合，它驱动从自旋液体相到拓扑带绝缘体的转变。由此产生的Kane-Mele-Hubbard模型打开了一系列研究的大门，这些研究解决了Z2拓扑绝缘子中的关联效应问题。在这里，我们将重点关注两个方面。螺旋边态的关联，以及在关联存在的情况下Z2拓扑绝缘体的一般表征。这些研究将依赖于无符号问题的辅助场量子蒙特卡罗方法，它允许我们精确地计算具有多达18×18个晶胞的晶格的静态和动态关联函数。

Topology in solid state physics relies on the idea that states of matter can be characterized by global quantities as opposed to local order parameters which encapsulate symmetry breaking. In this grant proposal, we will concentrate on quantum many-body phenomena where topology plays a dominant role. The gapped quantum spin liquid phase recently observed in the Hubbard model on the honeycomb lattice [1] calls for a characterization. Can it be described by a topological order parameter or is it a band insulator in disguise? To tackle this issue we will develop numerical methods to probe for topological degeneracy. We will also modify the model Hamiltonian so as to attempt to adiabatically continue the quantum spin liquid phase to known band-insulating states. One such modification of the Hamiltonian is to include a spin-orbit coupling which drives a transition from the spin liquid phase to a topological band insulator. The resulting Kane-Mele-Hubbard model opens the door to a number of investigations which address the issue of correlation effects in Z2 topological insulators. Here we will focus on two aspects. Correlations in the helical edge states, and the general characterization of Z2 topological insulators in the presence of correlations. The investigations will rely on sign-problem-free auxiliary field quantum Monte Carlo methods, which allow us to exactly compute static and dynamic correlation functions on lattices with up to 18 x 18 unit cells.