Matrix-product-state-based quantum impurity solvers

这个项目的目的是推进基于矩阵积态的量子杂质求解器的状态，即计算嵌入在可能由多个外部带组成的外部槽中的一簇相关位点的局部光谱函数。在FOR 1807的第一阶段，这些杂质解算器（基于切比雪夫多项式或时间演化的傅立叶变换，结合线性预测技术）的性能可以被推进到这样的程度，即首次可以使用矩阵积态来研究平衡动态平均场理论（DMFT），用于连续时间量子蒙特卡罗（CTQMC）难以获得的多位点多波段配置。目前在DMFT杂质求解领域处于领先地位。它还可以用来增强研究非平衡DMFT （NEQDMFT）的相互作用强度和时间尺度。在第二阶段，这些成果将被利用和扩展：(i)在主题方面，我们希望为钒酸盐化合物开发可靠的DMFT描述，为动态聚类近似（DCA）中的Hubbard模型开发零温度下CTQMC难以达到的相互作用强度，为铁的相图，以及其他感兴趣的材料出现；（ii）在方法学方面，我们希望系统地研究浴槽描述的改进，以最大限度地减少纠缠，优化性能和可描述系统，灵感来自基于矩阵乘积状态的量子化学的类似研究，以及DMFT循环中关键但困难的浴槽拟合程序的改进。

The purpose of this project is to advance the status of quantum impurity solvers that are based on matrix product states, i.e. to calculate the local spectral function for a cluster of correlated sites embedded in an external bath consisting possibly of multiple external bands. In the first phase of FOR 1807, the performance of such impurity solvers (either based on Chebyshev polynomials or the Fourier transformation of time-evolutions, combined with a linear prediction technique) could be pushed so far that for the first time equilibrium dynamical mean-field theory (DMFT) can be studied using matrix product states for multi-site multi-band configurations which are difficult to access by continuous-time Quantum Monte Carlo (CTQMC), the current leader in the field for impurity solvers for DMFT. It also could be used to strongly enhance the interaction strengths and time scales that can be studied non-equilibrium DMFT (NEQDMFT). In the second phase, these achievements are to be exploited and extended: (i) on the thematic side, we want to develop a reliable DMFT description for vanadate compounds, for the Hubbard model in the dynamical cluster approximation (DCA) for interaction strengths hard to reach by CTQMC at zero temperature, for the phase diagram of iron pnictides, and further materials of interest as they emerge; (ii) on the methodological side, we want to study systematically improvements in the description of the bath in order to minimize entanglement and optimize performance and describable systems, inspired by similar studies in quantum chemistry based on matrix-product states, and improvements in a crucial, but difficult bath-fitting procedure in the DMFT cycle.