Thermodynamics and Dynamics of Disordered Quantum Spin Systems with Long Range Interactions

具有长程相互作用的无序量子自旋系统的热力学和动力学

• 批准号: 408309204
• 负责人: Professor Dr. Stefan Kettemann
• 金额: --
• 依托单位: Department of Physics and Astronomy
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2018
• 资助国家: 德国
• 起止时间: 2017-12-31 至 2022-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/408309204?language=en
• 关键词: Thermodynamics; Dynamics; Disordered; Quantum; Spin

The purpose of this project is a systematic study of the thermodynamic and dynamic properties of disordered systems with local quantum degrees of freedom, such as spins and tunneling systems which are coupled by long range interactions. Such systems are ubiquitous in real materials, like metals with magnetic impurities, doped semiconductors and glassy systems. Donor spins are studied intensively as Qubits for quantum computers. However, their coherent control and readout will require a detailed understanding of the thermodynamic and dynamic properties of such systems. The combination of disorder and long range interactions makes this a challenging open problem of theoretical physics. One can expect a transition from localized quantum excitations to delocalized global excitations when tuning the system parameters such as the spin density, the power law of the long-range interactions and the local field strength. The methods we intend to use and develop to this end are modifications of the real space renormalisation group (RSRG) method in combination with a scaling analysis of the distribution of excitation energies, correlation functions and entanglement entropy. Employing numerical finite size scaling analysis, we will determine the critical parameters of the quantum phase transitions. We will study corrections to the RSRG, which will allow us to quantify the accuracy of the RSRG method and to calculate typical correlation functions such as the concurrence, for any distance r. We will compare these results with calculations obtained by a tensor network extension of the density matrix renormalization group method. We then plan to extend the analysis to models with mixed ferro- and antiferro-coupling. Extending the study to higher dimensions will enable us to model the properties of real systems and to analyze existing and future experimental results. Next, we study the dynamics after quantum quenches. First, we determine the quantum fidelity, the scalar product between the ground state of a spin system before and after a perturbation has been turned on, as function of the number of spins N. Then, we develop a combination of response theory and a dynamic variant of the SDRG method, where the RG rules are modified to account for the fact that triplet states couple to other spins. Thereby, we obtain the transient dynamics of the spin components for long range coupled disordered AFM spin systems and can study the relaxation dynamics and propagation of disturbances after quantum quenches.

该项目的目的是系统研究具有局部量子自由度的无序系统的热力学和动力学性质，例如通过长程相互作用耦合的自旋和隧道系统。这种系统在真实材料中普遍存在，例如含有磁性杂质的金属、掺杂半导体和玻璃系统。供体自旋作为量子计算机的量子位被深入研究。然而，它们的相干控制和读出将需要详细了解此类系统的热力学和动力学特性。无序和长程相互作用的结合使得这是一个具有挑战性的理论物理学开放问题。当调整自旋密度、长程相互作用的幂律和局部场强等系统参数时，可以预期从局域量子激发到离域全局激发的转变。为此，我们打算使用和开发的方法是对实空间重正化群（RSRG）方法的修改，结合激发能量、相关函数和纠缠熵分布的缩放分析。采用数值有限尺寸尺度分析，我们将确定量子相变的关键参数。我们将研究 RSRG 的修正，这将使我们能够量化 RSRG 方法的准确性并计算典型的相关函数，例如对于任何距离 r 的并发度。我们将这些结果与通过密度矩阵重整化群方法的张量网络扩展获得的计算结果进行比较。然后，我们计划将分析扩展到具有混合铁耦合和反铁耦合的模型。将研究扩展到更高的维度将使我们能够对真实系统的特性进行建模并分析现有和未来的实验结果。接下来，我们研究量子淬灭后的动力学。首先，我们确定量子保真度，即扰动开启之前和之后自旋系统基态之间的标量积，作为自旋数量 N 的函数。然后，我们开发了响应理论和动态理论的结合。 SDRG 方法的变体，其中修改 RG 规则以考虑三重态与其他自旋耦合的事实。由此，我们获得了长程耦合无序AFM自旋系统的自旋分量的瞬态动力学，并可以研究量子淬灭后的弛豫动力学和扰动的传播。