Iterative path integral summation for nonequilibrium quantum transport
Iterative path integral summation for nonequilibrium quantum transport
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非平衡量子输运的迭代路径积分求和
DOI：
10.1002/pssb.201349187
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
M. Thorwart
中科院分区：
文献类型：
--
作者：
S. Weiss;R. Hützen;D. Becker;J. Eckel;R. Egger;M. Thorwart
我们发展了一种数值精确的方法来计算非平衡量子输运问题的实时路径积分表达式。该方案基于感兴趣的非平衡观测的母函数的路径积分(ISPI)的确定性迭代求和。我们将该方案应用于计算作为量子点或隧道耦合到引线的分子的小的强关联量子系统的电荷流或动态量。由于引线在时间上是非局部的，因此在有限的记忆时间内充分考虑了自能，从而包括了非马尔可夫效应。数值结果首先外推到消失(特罗特)时间离散，然后外推到无限记忆时间。该方法首先应用于单杂质Anderson点的非平衡输运。我们在丰富参数空间的不同制度下对我们的结果进行了基准测试。在各自的有效性机制中，实时路径积分(ISPI)的迭代求和结果与其他最先进方法的结果相匹配。特别是，我们选择了Anderson模型的混合价体系，将ISPI与含时密度矩阵重整化群(TDMRG)和泛函RG计算进行了比较。其次，我们确定了在存在振动模的情况下通过分子结的非平衡电流。我们发现了单杂质Anderson-Holstein模型到有效自旋1问题的精确映射。在分析容易处理的区域，如绝热声子或弱分子-铅耦合区域，我们复制了已知的微扰结果。研究这些极限之间的交叉机制表明，弗兰克-康登封锁持续存在于量子极限中。在低温下，由于非平衡条件，特性中的Franck-Condon阶跃被涂抹。这里研究的第三个系统是磁安德森模型，它由一个自旋的单轨道量子点和一个包含自旋1/2磁性杂质的量子点组成。库仑相互作用以及磁性杂质与电子自旋的交换耦合对动力学有很大影响。我们研究了通过该系统的非平衡隧穿电流作为交换和库仑相互作用以及实时杂质极化的函数。从物理可观测量的实时演化中，我们能够确定含时非平衡电流的特征和杂质的驰豫动力学。这些例子表明，当所有的时间和能量尺度都是相同的数量级时，ISPI技术特别适合于量子体制。
We have developed a numerically exact approach to compute real‐time path integral expressions for quantum transport problems out of equilibrium. The scheme is based on a deterministic iterative summation of the path integral (ISPI) for the generating function of nonequilibrium observables of interest. We apply the scheme to compute the charge current or dynamical quantities of small strongly correlated quantum systems as a quantum dot or molecules that are tunnel coupled to leads. Self‐energies due to the leads, being nonlocal in time, are fully taken into account within a finite memory time, thereby including non‐Markovian effects. Numerical results are extrapolated first to vanishing (Trotter) time discretization and, second, to infinite memory time. The method is applied to nonequilibrium transport through a single‐impurity Anderson dot in the first place. We benchmark our results in various regimes of the rich parameter space. In the respective regime of validity, iterative summation of real‐time path integrals (ISPI) results are shown to match those of other state‐of‐the art methods. Especially, we have chosen the mixed valence regime of the Anderson model to compare ISPI to time dependent density matrix renormalization group (tDMRG) and functional RG calculations. Secondly, we determine the nonequilibrium current through a molecular junction in presence of a vibrational mode. We have found an exact mapping of the single impurity Anderson–Holstein model to an effective spin‐1 problem. In analytically tractable regimes, as the adiabatic phonon or weak molecule‐lead coupling regime, we reproduce known perturbative results. Studying the crossover regime between those limits shows that the Franck–Condon blockade persists in the quantum limit. At low temperature, the Franck–Condon steps in the characteristics are smeared due to nonequilibrium conditions. The third system under investigation here is the magnetic Anderson model which consists of a spinful single‐orbital quantum dot with an incorporated quantum mechanical spin–1/2 magnetic impurity. Coulomb interaction together with the exchange coupling of the magnetic impurity with the electron spins strongly influence the dynamics. We investigate the nonequilibrium tunneling current through the system as a function of exchange and Coulomb interaction as well as the real‐time impurity polarization. From the real‐time evolution of physical observables, we are able to determine characteristics of the time‐dependent nonequilibrium current and the relaxation dynamics of the impurity. These examples illustrate that the ISPI technique is particularly well suited for the quantum regime, when all time and energy scales are of the same order of magnitude.
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