Advanced wave-function based methods for electron-phonon coupled systems

本项目的主要目标是开发高效和通用的计算方法，用于研究具有强波动玻色子自由度的相关低维量子系统。这些方法主要基于低维量子多体系统中最强大的方法之一——量子态的矩阵积态表示。在第一个资助期，我们开发，实施和测试了数值方法，使我们能够研究玻色子系统的非平衡动力学。在第二个资助期，我们将提高这些方法在平衡和不平衡系统中的效率。此外，我们计划在凝聚态物理的各种及时问题中调整和测试我们的算法，这些问题主要与电子-声子系统有关。这些应用包括相变和局部纠缠熵，通过电子-声子耦合纳米结构的非平衡和耗散输运，时间分辨光谱和光致一维材料的相变，以及自旋-声子耦合模型中的自旋输运。

The main goal of this project is the development of efficient and versatilecomputational methods for studying correlated low-dimensional quantum systemswith strongly fluctuating bosonic degrees of freedom. These methods are mainly based on one of the most powerful approaches for low-dimensional quantum many-body systems, the matrix-product-state representation of quantumstates. In the first funding period, we developed, implemented and tested numerical methods which allowed us to study the nonequilibrium dynamics of bosonic systems. In the second funding period we will improve the efficiency of these methods for systems in and out-of-equilibrium. In addition, we plan to adapt and test our algorithms in a broad variety of timely problems from condensed matter physics, mostly related to electron-phonon systems. These applications include phase transitions and local entanglement entropy, nonequilibrium and dissipative transport through electron-phonon coupled nanostructures, time-resolved spectroscopy and photoinduced phase transitions inquasi-one-dimensional materials, as well as spin transport in spin-phonon coupled models.