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首页> 外文期刊>The journal of physical chemistry, A. Molecules, spectroscopy, kinetics, environment, & general theory >Iterative Calculation of Energy Eigenstates Employing the Multilayer Multiconfiguration Time-Dependent Hartree Theory
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Iterative Calculation of Energy Eigenstates Employing the Multilayer Multiconfiguration Time-Dependent Hartree Theory

机译：多层多配置时变Hartree理论的能量本征态迭代计算

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摘要

The improved relaxation approach of Meyer and co-workers is extended by employing the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) theory. Within this approach the trial wave function is expressed by a recursive, multilayered expansion that is the same as in a normal ML-MCTDH simulation. Calculation of an energy eigenstate then proceeds by iteratively diagonalizing the Boltzmann operator in the top layer representation using a Lanczos/Arnoldi method while relaxing the single particle functions of all layers using the ML-MCTDH imaginary time propagation. Numerical iteration is stopped until the relative energy and/or density of the target state meet the convergence criteria. The application of this multilayer improved relaxation method is illustrated by computing the energy splitting for the lowest pair of eigenstates as well as the spin observables and entanglement entropy of the spin-boson model. A large number of degrees of freedom, up to 10 000 bath modes, can be treated, and thus the appropriate phase transition at a critical system-bath coupling strength may be predicted via appropriate extrapolations.
机译：Meyer和同事的改进的放松方法通过采用多层多配置时变哈特里（ML-MCTDH）理论进行了扩展。在这种方法中，试验波函数由递归的多层扩展表示，与常规ML-MCTDH仿真中的相同。然后，通过使用Lanczos / Arnoldi方法对顶层表示中的Boltzmann算子进行迭代对角化来进行能量本征态的计算，同时使用ML-MCTDH虚构时间传播来放宽所有层的单个粒子函数。停止数值迭代，直到目标状态的相对能量和/或密度满足收敛标准为止。通过计算最低的本征态对的能量分裂以及自旋玻色子模型的自旋可观量和纠缠熵来说明这种多层改进的松弛方法的应用。可以处理多达10万个浴模的大量自由度，因此可以通过适当的外推法预测在临界系统-浴耦合强度下的适当相变。

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