Finite-Temperature Dynamics with Matrix Product State and Cluster Approaches

使用矩阵积状态和簇方法的有限温度动力学

• 批准号: 299367771
• 负责人: Professorin Dr. Maria Daghofer
• 金额: --
• 依托单位: Institut für Theoretische Physik
• 依托单位国家: 德国
• 项目类别: Research Units
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/299367771?language=en
• 关键词: Finite; Temperature; Dynamics; Matrix; Product

A variety of experimental probes is available for the investigation of dynamic susceptibilities. By indicating the allowed excitations of a system, these quantities often permit us to establish the properties of the quantum state. To do so, we however also need theoretical access to the spectra of appropriate effective low-energy models. The present proposal aims at extending the range of available numerical tools for this task. In particular, we plan to address finite temperatures in order to investigate signatures of ordered phases as opposed to disordered high-temperature states. Matrix Product State approaches (MPS) and cluster techniques like the Cluster Perturbation Theory (CPT) and the Variational Cluster Approximation (VCA) can be used to treat strongly correlated quantum systems at finite temperatures, but have so far mostly been applied to the ground state at T = 0. In this project, we plan to extend the range of applicability of both methods to treat spin and electron systems at finite temperatures in two-dimensional (2D) and quasi-2D geometries, to compare their predictive power, and to use MPS approaches at finite temperature as cluster solver. This will lead to cluster methods for 2D systems working at finite temperature and being more reliable since the results will be based on larger clusters. In particular we plan to focus on finite-temperature dynamical spectral functions, which are directly accessible via experiments like, e.g., neutron scattering, angle-resolved photo-electron spectroscopy (ARPES) or resonant inelastic X-ray scattering (RIXS). The goal is to predict signatures expected for spin or electron systems (e.g., iridate systems) in topologically nontrivial phases and to investigate them as they go through phase transitions from trivial to nontrivial states.

有多种实验探针可用于动态敏感性的研究。通过指示系统允许的激发，这些量通常允许我们建立量子态的属性。然而，要做到这一点，我们还需要从理论上了解适当的有效低能量模型的光谱。本提案旨在扩展用于此任务的可用数值工具的范围。特别是，我们计划解决有限温度问题，以便研究有序相的特征，而不是无序的高温状态。矩阵积态方法 (MPS) 以及簇微扰理论 (CPT) 和变分簇近似 (VCA) 等簇技术可用于处理有限温度下的强相关量子系统，但迄今为止大多应用于基态在 T = 0 时。在这个项目中，我们计划扩展这两种方法的适用范围，以在二维 (2D) 和准 2D 几何形状的有限温度下处理自旋和电子系统，以比较它们的预测能力，并在有限温度下使用 MPS 方法作为集群求解器。这将导致二维系统的聚类方法在有限温度下工作并且更加可靠，因为结果将基于更大的聚类。我们特别计划关注有限温度动态光谱函数，这些函数可以通过中子散射、角分辨光电子能谱 (ARPES) 或共振非弹性 X 射线散射 (RIXS) 等实验直接获得。目标是预测拓扑非平凡相中自旋或电子系统（例如虹膜系统）的预期特征，并在它们经历从平凡状态到非平凡状态的相变时对其进行研究。