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

本项目的目的是系统地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，例如由远程相互作用耦合的自旋和隧道系统。这样的系统在真实的材料中无处不在，比如带有磁性杂质的金属、掺杂半导体和玻璃系统。供体自旋作为量子计算机的量子比特被深入研究。然而，它们的相干控制和读出将需要对此类系统的热力学和动力学特性有详细的了解。无序和远距离相互作用的结合使这成为理论物理学中一个具有挑战性的开放性问题。当调整系统参数，如自旋密度、远程相互作用的幂律和局部场强时，可以预期从局域量子激发到非局域全局激发的转变。为此，我们打算使用和发展的方法是对实空间重整化群（RSRG）方法的修改，并结合对激发能、相关函数和纠缠熵分布的标度分析。采用数值有限尺度分析，我们将确定量子相变的关键参数。我们将研究对RSRG的修正，这将使我们能够量化RSRG方法的准确性，并计算任何距离r的典型相关函数，如并发。我们将把这些结果与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模拟真实系统的特性，并分析现有和未来的实验结果。接下来，我们研究了量子猝灭后的动力学。首先，我们确定了量子保真度，即自旋系统在扰动启动前后基态之间的标量乘积，作为自旋数n的函数。然后，我们开发了响应理论和SDRG方法的动态变体的组合，其中修改了RG规则以考虑三重态与其他自旋耦合的事实。由此，我们获得了远程耦合无序AFM自旋系统自旋组分的瞬态动力学，并可以研究量子猝灭后扰动的弛豫动力学和传播。

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.