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

拓扑带绝缘体中自旋液体和相关诱导效应的量子蒙特卡罗研究

• 批准号: 216711240
• 负责人: Professor Dr. Fakher Fakhry Assaad
• 金额: --
• 依托单位: Lehrstuhl für Theoretische Physik I - Festkörperphysik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2013
• 资助国家: 德国
• 起止时间: 2012-12-31 至 2016-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/216711240?language=en
• 关键词: Quantum; Monte; Carlo; studies; spin

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.

固体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，而不是由包含对称性破缺的局部序参量来表征。在这个资助计划中，我们将集中研究拓扑学起主导作用的量子多体现象。最近在Hubbard模型中观察到的蜂窝晶格上的带隙量子自旋液相[1]需要表征。它能用拓扑序参量来描述吗？或者它是一个伪装的带状绝缘体？为了解决这个问题，我们将发展数值方法来探测拓扑退化。我们也将修改模型的哈密顿量，以便尝试将量子自旋液相连续到已知的带绝缘态。一个这样的修改的哈密顿量是包括一个自旋轨道耦合，驱动从自旋液相的拓扑带绝缘体的转变。由此产生的凯恩-梅勒-哈伯德模型打开了大门，一些调查，解决问题的相关效应在Z2拓扑绝缘体。在这里，我们将重点关注两个方面。螺旋边缘态的相关性，以及相关性存在下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，该方法使我们能够精确计算具有高达18 x 18个单位单元的晶格上的静态和动态相关函数。