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.

可用于研究动态敏感性的各种实验探针。通过指示系统的激发，这些数量通常使我们能够确定量子状态的特性。为此，我们还需要理论上访问适当有效的低能模型的光谱。本提案旨在扩展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，以研究有序阶段的特征，而不是高温状态。矩阵产品状态方法（MPS）和集群技术（例如簇扰动理论（CPT）和变化群集近似（VCA）可用于治疗在有限温度下在有限的温度下在有限的温度下进行密切相关的量子系统，但到目前为止，在t = 0的基础状态下，在此项目中都应用了两种范围。 （2d）和Quasi-2d几何形状，以比较其预测能力，并在有限温度下使用MPS方法作为群集求解器。这将导致在有限温度下工作的2D系统的群集方法，并且更可靠，因为结果将基于较大的簇。特别是，我们计划专注于有限的动态频谱函数，这些函数可以通过实验直接访问，例如，例如中子散射，角度分辨光电子光谱（ARPES）或谐振剂X射线散射（RIXS）。目的是预测拓扑或电子系统（例如，偶然系统）的签名，并在拓扑阶段进行了调查，并在它们经过从琐事到非平凡状态的相变时进行调查。