Christov Ivan P
Physics Department, Sofia University, 1164 Sofia, Bulgaria.
Institute of Electronics, Bulgarian Academy of Sciences, 1784 Sofia, Bulgaria.
Entropy (Basel). 2021 Jul 7;23(7):868. doi: 10.3390/e23070868.
The time-dependent quantum Monte Carlo method for fermions is introduced and applied in the calculation of the entanglement of electrons in one-dimensional quantum dots with several spin-polarized and spin-compensated electron configurations. The rich statistics of wave functions provided by this method allow one to build reduced density matrices for each electron, and to quantify the spatial entanglement using measures such as quantum entropy by treating the electrons as identical or distinguishable particles. Our results indicate that the spatial entanglement in parallel-spin configurations is rather small, and is determined mostly by the spatial quantum nonlocality introduced by the ground state. By contrast, in the spin-compensated case, the outermost opposite-spin electrons interact like bosons, which prevails their entanglement, while the inner-shell electrons remain largely at their Hartree-Fock geometry. Our findings are in close correspondence with the numerically exact results, wherever such comparison is possible.
介绍了用于费米子的含时量子蒙特卡罗方法，并将其应用于计算具有几种自旋极化和自旋补偿电子构型的一维量子点中电子的纠缠。该方法提供的丰富波函数统计信息使人们能够为每个电子构建约化密度矩阵，并通过将电子视为全同或可区分粒子，使用量子熵等度量来量化空间纠缠。我们的结果表明，平行自旋构型中的空间纠缠相当小，并且主要由基态引入的空间量子非局域性决定。相比之下，在自旋补偿的情况下，最外层的反自旋电子像玻色子一样相互作用，这主导了它们的纠缠，而内壳层电子在很大程度上保持在它们的哈特里 - 福克几何构型。在可能进行比较的任何地方，我们的发现都与数值精确结果密切相符。
