Nonequilibrium dynamics in 2D clusters from the perspective of quantum typicality and eigenstate thermalization

从量子典型性和本征态热化的角度研究二维团簇中的非平衡动力学

• 批准号: 397067869
• 负责人: Professorin Dr. Kristel Michielsen
• 金额: --
• 依托单位: Jülich Supercomputing Centre (JSC)
• 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/397067869?language=en
• 关键词: Nonequilibrium; dynamics; 2D; clusters; perspective

Understanding fundamental aspects of the physics of many-body systems out of equilibrium is both, highly desired and notoriously difficult. In particular, explaining the occurrence of statistical behavior in isolated quantum systems continues to be a challenge to theory, including the derivation of omnipresent phenomena such as exponential relaxation, diffusion, equilibration, and thermalization from truly microscopic principles. Recent and substantial progress in this context is also related to the emergent concept of quantum typicality and the celebrated eigenstate thermalization hypothesis (ETH). While quantum typicality means in essence that an ensemble average is accurately given by an expectation value of just a single pure state drawn at random from a high-dimensional Hilbert space, the (diagonal part of the) ETH ansatz assumes such type of typicality even on the level of individual energy eigenstates.In this project, we build on our previous works, e.g., on our works in the first fundingperiod of this research unit, and plan to study nonequilibrium dynamics in two-dimensional (2D) clusters from the perspective of quantum typicality and ETH. In our study, we will heavily rely on the use of dynamical quantum typicality (DQT) and state-of-the-art (super) computing to tackle these 2D clusters, ranging from finite systems of interacting spins in a rectangular geometry, like two-leg or multi-leg ladders, to square lattices. Moreover, we will complement our analysis by a combination of DQT with projection operator techniques and numerical linked-cluster expansions (NCLE). Especially the latter combination of DQT with NLCE has the promising potential to shed light onto the physics of extended 2D models, with or without disorder. In this way, we might be able to contribute to the question of many-body localization in higher dimensions.While a significant body of research in our project is devoted to transport quantities withinthe framework of linear response theory, another equally important question constitutes the role of the specific initial condition for the subsequent relaxation process. In this context, we will scrutinize our current proposal that the (off-diagonal part of the) ETH ansatz implies a "universal" relation between the dynamics far away from and close to equilibrium, by performing several cases studies beyond idealized models of random-matrix type. In the same context, our extension to observables of non-transport type also allows us to explore in how far typicality-based predictions for the entire relaxation process, essentially related to survival probabilities, apply to generic nonequilibrium situations.

了解多体系统的物理学的基本方面的平衡是，高度期望和众所周知的困难。特别是，解释孤立量子系统中统计行为的发生仍然是对理论的挑战，包括从真正的微观原理推导出无所不在的现象，如指数弛豫，扩散，平衡和热化。最近在这方面取得的重大进展也与量子典型性的涌现概念和著名的本征态热化假设（ETH）有关。虽然量子典型性本质上意味着系综平均值由从高维希尔伯特空间随机抽取的单个纯态的期望值精确给出，但ETH分析的（对角线部分）即使在单个能量本征态的水平上也假设了这种类型的典型性。在这个项目中，我们建立在我们以前的工作基础上，例如，在本研究单元第一个资助期的工作基础上，计划从量子典型性和ETH的角度研究二维团簇的非平衡动力学。在我们的研究中，我们将严重依赖于使用动态量子典型性（DQT）和最先进的（超级）计算来处理这些2D集群，从矩形几何中相互作用的自旋有限系统，如双腿或多腿梯子，到正方形晶格。此外，我们将补充我们的分析相结合的DQT与投影算子技术和数值连接集群扩展（NCLE）。特别是后者的DQT与NLCE的组合有前途的潜力，揭示了扩展的2D模型的物理，有或没有无序。通过这种方式，我们也许能够对高维多体局域化问题做出贡献。虽然我们项目中的一个重要研究主体致力于线性响应理论框架内的输运量，但另一个同样重要的问题是特定初始条件对随后的弛豫过程的作用。在这种情况下，我们将仔细研究我们目前的建议，即ETH的（非对角部分）的反演算法意味着远离和接近平衡的动态之间的“普遍”关系，通过执行几个案例研究超越随机矩阵类型的理想化模型。在同样的背景下，我们的扩展到非运输型的观测值也使我们能够探索在多大程度上典型的基于预测的整个松弛过程，基本上与生存概率，适用于一般的非平衡状态。