Finite-Temperature Dynamics with Matrix Product State and Cluster Approaches

各种实验探头可用于动态磁化率的调查。通过指示系统的允许激发，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获得适当的有效低能模型的光谱。本建议旨在扩大这一任务可用的数字工具的范围。特别是，我们计划解决有限的温度，以调查签名的有序相，而不是无序的高温状态。矩阵乘积态方法（MPS）和簇技术（如簇微扰理论（CPT）和变分簇近似（VCA））可以用于处理有限温度下的强关联量子系统，但迄今为止大多数应用于T = 0的基态。在这个项目中，我们计划扩大这两种方法的适用范围，以处理自旋和电子系统在有限温度下的二维（2D）和准二维几何形状，比较它们的预测能力，并使用MPS方法在有限温度下作为集群求解器。这将导致用于在有限温度下工作的2D系统的聚类方法，并且由于结果将基于更大的聚类而更可靠。特别是，我们计划专注于有限温度动力学谱函数，这是直接通过实验，如，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）。目标是预测自旋或电子系统预期的特征（例如，虹膜系统）在拓扑非平凡的阶段，并调查他们，因为他们通过从平凡到非平凡状态的相变。

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.