arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1902.06606cond-mat.str-el
收藏

强关联材料的计算研究和动力学研究

Computational Studies and Algorithmic Research of Strongly Correlated Materials

Zhuoran He

摘要:

本博士论文主要研究具有局域电子轨道的强关联材料。我们研究了两种实际材料(LuNiO $_3$和VO $_2$)和一种模型体系,安德森杂质模型论文分为两个部分。在第一部分中,我们使用密度泛函理论+ $U$方法,计算了稀土镍酸盐的LuNiO $_3$在衬底诱导应变下的平衡相变和窄禁带莫特绝缘体的VO $_2$在激光脉冲诱导光激发下的非平衡相变。添加$U$的效果在两种材料中表现为响应于电子轨道占据率的变化的能带结构的变化,即,软带效应。这种效应引起不同轨道之间的电子竞争,产生多个亚稳态。在第二部分中,我们超越能带理论,研究了如何利用基于矩阵乘积态(MPS)的密度矩阵重整化群(DMRG)方法对Anderson杂质模型进行实时演化,以建立非平衡动力学平均场理论(DMFT)的实时杂质求解器为目标。我们研究了淬火和周期驱动的单杂质安德森模型(SIAM),并获得了一些复杂性的结果的基础上,我们在论文中开发的DMRG(4-MPS方法)的非标准实现。我们发现在SIAM的星形几何中,MPS中浴轨道的有序性显著影响纠缠熵的增加,从而影响模拟的计算复杂度。

英文摘要:

This PhD thesis conducts a focused study of strongly correlated materials with localized electron orbitals. We have studied two real materials (LuNiO$_3$ and VO$_2$) and one model system, i.e., the Anderson impurity model. The thesis is divided into two parts. In the first part, we use the DFT+$U$ method, to calculate the equilibrium phase transitions of LuNiO$_3$ as an example of rare-earth nickelates under a substrate-induced strain, and the nonequilibrium phase transitions of VO$_2$ as an example of narrow-gap Mott insulators under laser-pulse-induced photoexcitations. The effect of adding $U$ is manifested in both materials as the change of band structure in response to the change of orbital occupancies of electrons, i.e., the soft band effect. This effect brings about competitions of electrons between different orbitals and gives rise to multiple metastable states. In the second part, we go beyond band theory and study how we can use the density matrix renormalization group (DMRG) method based on matrix product states (MPS) to perform real-time evolutions of the Anderson impurity model, towards the goal of building a real-time impurity solver for the nonequilibrium dynamical mean-field theory (DMFT). We study both the quenched and periodically driven single-impurity Anderson models (SIAM) and have obtained some complexity results based on a non-standard implementation of DMRG (the 4-MPS method) we developed in the thesis. We find in the star geometry of the SIAM that the ordering of the bath orbitals in the MPS affects dramatically the increase of entanglement entropy and thus the computational complexity of the simulation.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑