Approach to equilibrium in interacting flat band systems

相互作用平带系统的平衡方法

基本信息

项目摘要

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.
最近在理论和实验上对表现出多体定位(MBL)的系统进行了研究,因为它们可以保留一些初始条件的记忆,因此对于存储量子信息很有意义。 MBL 可以被视为安德森定位对交互系统的推广,因此通常被讨论为发生在无序系统中。然而,有人提出了在平移不变系统中实现 MBL 的可能性,特别是最近在这方面考虑了平带系统。非相互作用平带系统的特征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存在局部静止本征态。因此,平带是这些系统中不同的局域化来源,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,该系统在存在粒子-粒子相互作用的情况下具有局域化。在这个项目中,我们想要研究这种相互作用的平带系统如何平衡以及在什么条件下它们不会热化。在之前的工作中,我们已经确定了一种金刚石梯子,其中平带在存在相互作用的情况下仍然存在。我们能够证明,该系统违反了本征态热化假说(ETH),并且所选初始状态的参与率在很长一段时间内保持较小,这表明多体局域状态。最近,Danieli 等人提出了一种方案,如何通过所谓的半解缠哈密顿量的酉变换生成相互作用的平带哈密顿量。这里将考虑此类模型。除了测试 ETH 和参与率之外,我们还想确定不均匀密度分布的松弛动力学,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)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及其演变方式。这将与无序 MBL 系统中已知的行为进行比较,其中已知会发生次扩散。此外,我们还计划研究无序对相互作用平带系统的影响,以更好地理解从平带定位到无序引起的 MBL 的交叉。

项目成果

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Professor Dr. Thomas Dahm其他文献

Professor Dr. Thomas Dahm的其他文献

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{{ truncateString('Professor Dr. Thomas Dahm', 18)}}的其他基金

Thin-film hybrid structures of topological insulators with superconductors and ferromagnets: experiment and theory
拓扑绝缘体与超导体和铁磁体的薄膜混合结构:实验与理论
  • 批准号:
    314727505
  • 财政年份:
    2016
  • 资助金额:
    --
  • 项目类别:
    Priority Programmes
Phasensensitive Tests der Ordnungsparameter-Symmetrie in unkonventionellen Supraleitern auf der Basis des Josephsoneffekts und gebundener Andreev-Zustände
基于约瑟夫森效应和束缚安德烈夫态的非常规超导体有序参数对称性相敏测试
  • 批准号:
    26479100
  • 财政年份:
    2006
  • 资助金额:
    --
  • 项目类别:
    Research Grants

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