Approach to equilibrium in interacting flat band systems

相互作用平带系统的平衡方法

• 批准号: 397171440
• 负责人: Professor Dr. Thomas Dahm
• 金额: --
• 依托单位: Arbeitsgruppe Theorie der Kondensierten Materie
• 依托单位国家: 德国
• 项目类别: Research Units
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/397171440?language=en
• 关键词: Approach; equilibrium; interacting; flat; band

Systems that exhibit many-body localization (MBL) have been studied recently both theoretically and experimentally, because they can retain some memory of the initial conditions and are thus of interest for storing quantum information. MBL can be viewed as a generalization of Anderson localization to interacting systems and thus usually is discussed to occur in disordered systems. However, the possibility to achieve MBL in translationally invariant systems has been suggested and in particular, flat band systems have been considered in this context recently. Noninteracting flat band systems are characterized by the presence of flat energy dispersions and thus possess highly degenerate energy eigenstates. This in turn allows localized stationary eigenstates in the system. As a result, the flat band is a different source of localization in these systems and could equally well (instead of Anderson localization) lead to interacting many-body quantum systems that possess localization in the presence of particle-particle interactions.In this project we want to study, how such interacting flat band systems equilibrate and under what conditions they do not thermalize. In a previous work we have identified a diamond ladder in which the flat bands survive in the presence of interaction. We were able to demonstrate that the eigenstate thermalization hypothesis (ETH) is violated in this system and the participation ratio of selected initial states remains small over long times, which indicates a many-body localized state.Recently, Danieli et al have suggested a scheme, how interacting flat band Hamiltonians can be generated by unitary transformations from so-called semi-detangled Hamiltonians. Such models will be considered here. Besides testing ETH and the participation ratio we would like to determine the relaxation dynamics for inhomogeneous density distributions and see whether an unusual type of diffusion is present in these systems. We will use dynamical quantum typicality (DQT) to study the relaxation dynamics numerically.We plan to study the transition from the localized regime to an ergodic regime and how it evolves. This will be compared with the behavior known from disordered MBL systems, where subdiffusion is known to occur. Also, we plan to investigate the influence of disorder on interacting flat band systems to better understand the cross-over from flat band localization to disorder induced MBL.

表现出多体局域化（MBL）的系统最近在理论和实验上都得到了研究，因为它们可以保留一些初始条件的记忆，因此对存储量子信息感兴趣。MBL可以被看作是安德森局域化到相互作用系统的推广，因此通常被讨论发生在无序系统中。然而，已经提出了在非线性不变系统中实现MBL的可能性，特别是最近在这方面已经考虑了平带系统。非相互作用的平带系统的特征在于存在平坦的能量色散，因此具有高度简并的能量本征态。这反过来又允许系统中的局部固定本征态。因此，平带是这些系统中局域化的一个不同来源，并且同样可以（而不是安德森局域化）导致相互作用的多体量子系统，这些系统在粒子-粒子相互作用的存在下具有局域化。在这个项目中，我们想研究，这种相互作用的平带系统是如何平衡的，以及在什么条件下它们不会热化。在以前的工作中，我们已经确定了一个钻石阶梯中的平面带生存的相互作用。我们证明了该系统不满足本征态热化假设（ETH），并且在很长时间内选择的初始态的参与率很小，这表明该系统是一个多体局域态。最近，Danieli等人提出了一个方案，即如何通过幺正变换从所谓的半解缠哈密顿量生成相互作用平带哈密顿量。这里将考虑这些模型。除了测试ETH和参与率，我们还想确定非均匀密度分布的弛豫动力学，看看这些系统中是否存在不寻常的扩散类型。我们将使用动力学量子典型性（DQT）来数值研究弛豫动力学，我们计划研究从局域态到遍历态的转变以及它是如何演变的。这将与已知的行为从无序MBL系统，其中亚扩散是已知的发生。此外，我们计划调查的影响，相互作用的平带系统的障碍，以更好地了解交叉从平带本地化的障碍诱导MBL。