投影密度矩阵嵌入理论的多碎片实时扩展：扩展体系中的非平衡电子动力学
A multi-fragment real-time extension of projected density matrix embedding theory: Non-equilibrium electron dynamics in extended systems
AI总结：
本文提出投影密度矩阵嵌入理论的多碎片实时扩展，通过同时传播碎片-浴嵌入波函数与全局平均场波函数，并施加1-RDM匹配条件，实现了对扩展强关联体系中非平衡电子动力学的准确高效模拟，在Anderson模型上验证了其相比TDHF的显著改进和随碎片增大快速收敛至精确动力学的性能。
摘要：
在这项工作中，我们推导了投影密度矩阵嵌入理论（pDMET）的多碎片实时扩展，旨在处理强关联体系中的非平衡电子动力学。与先前发展的静态pDMET一样，实时pDMET将整个体系划分为许多碎片；每个碎片与体系其余部分之间的耦合通过以量子浴形式对环境进行紧凑表示来处理。实时pDMET涉及同时传播每个独立碎片-浴嵌入体系的波函数以及整个体系的辅助平均场波函数。运动方程通过以下方式推导：（i）在与每个独立碎片相关联的碎片和浴空间中投影含时薛定谔方程，以及（ii）在所有时间点上强制执行从碎片计算获得的全局单粒子约化密度矩阵（1-RDM）与平均场1-RDM之间的pDMET匹配条件。该方法的准确性通过与时间依赖密度矩阵重整化群（TD-DMRG）和时间依赖Hartree-Fock（TDHF）理论的比较进行基准测试；这些方法被应用于单杂质Anderson模型以及具有有序和无序杂质分布的多杂质Anderson模型。结果表明，与TDHF相比有大幅改进，并且随着碎片尺寸的增加，能够快速收敛到精确动力学。我们的结果表明，实时pDMET是一种有前景且灵活的方法，可用于模拟大尺寸异质体系中的非平衡电子动力学。
英文摘要：
In this work, we derive a multi-fragment real-time extension of projected density matrix embedding theory (pDMET) designed to treat non-equilibrium electron dynamics in strongly correlated systems. As in the previously developed static pDMET, real-time pDMET partitions the total system into many fragments; the coupling between each fragment and the rest of the system is treated through a compact representation of the environment in terms of a quantum bath. Real-time pDMET involves simultaneously propagating the wavefunctions for each separate fragment-bath embedding system along with an auxiliary mean-field wavefunction of the total system. The equations of motion are derived by (i) projecting the time-dependent Schrodinger equation in the fragment and bath space associated with each separate fragment and by (ii) enforcing the pDMET matching conditions between the global 1-particle reduced density matrix (1-RDM) obtained from the fragment calculations and the mean-field 1-RDM at all points in time. The accuracy of the method is benchmarked through comparisons to the time-dependent density-matrix renormalization group (TD-DMRG) and time-dependent Hartree-Fock (TDHF) theory; the methods were applied to a single-impurity Anderson model and multi-impurity Anderson models with ordered and disordered distributions of the impurities. The results demonstrate a large improvement over TDHF and rapid convergence to the exact dynamics with an increase in fragment size. Our results demonstrate that real-time pDMET is a promising and flexible method to simulate non-equilibrium electron dynamics in heterogeneous systems of large size.
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