Approach to equilibrium in interacting flat band systems

表现出多体定位（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很感兴趣。MBL可以看作是安德森定位对相互作用系统的推广，因此通常讨论发生在无序系统中。然而，已经提出了在平移不变系统中实现MBL的可能性，特别是最近在此背景下考虑了平带系统。非相互作用的平带系统的特点是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定域平稳特征态。因此，平带在这些系统中是一个不同的局域化来源，并且同样可以很好地（而不是安德森局域化）导致相互作用的多体量子系统在粒子-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发热。在之前的工作中，我们已经确定了一个钻石阶梯，其中的平带在相互作用下存活下来。我们能够证明该系统违背了本征态热化假设（ETH），并且所选初始态的参与比例在长时间内保持较小，表明该系统是多体局域态。最近，Danieli等人提出了一种方案，如何通过所谓的半纠缠哈密顿量的幺正变换产生相互作用的平坦带哈密顿量。这里将考虑这些模型。除了测试ETH和参与比外，我们还想确定非均匀密度分布的弛豫动力学，并看看这些系统中是否存在不寻常的扩散类型。我们将使用动态量子典型性（DQT）对弛豫动力学进行数值研究。我们计划研究从局部状态到遍历状态的转变以及它是如何演变的。这将与已知发生亚扩散的无序MBL系统的行为进行比较。此外，我们计划研究无序对相互作用的平带系统的影响，以更好地理解从平带定位到无序诱导MBL的交叉。

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.