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

点击翻译按钮获取中文摘要

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.