两端纳米器件系统中非平衡态电子的量子纠缠度量研究

电子器件已发展到纳米尺寸，进入量子区域。作为量子系统的本质特性，量子纠缠与量子器件的行为高度关联，其度量已经成为预测量子相变等临界行为的主要工具，对新型量子器件的研制和理解意义重大，已在两端纳米器件系统的研究中倍受关注。然而，传统研究纠缠的多体密度矩阵方法的复杂度随系统尺度指数增加，在面对器件中经常出现的非平衡状态和多电子特性时非常困难。本项目中，我们计划通过非平衡格林函数方法，将多体问题转化为复杂度与系统尺度成正比的单体问题；通过计算电子的关联函数矩阵，将在平衡态建立的纠缠熵度量方法推广到非平衡态两端纳米器件系统。当前，获取纠缠熵的关联函数矩阵方法已经成熟。将多体问题转化为单体问题的非平衡格林函数方法，在研究器件量子输运方面也已获得巨大成功，它与密度泛函理论的结合是下一代器件模拟与设计的主要候选方法。我们将以此为基础，进一步研究具体材料系统的量子纠缠度量及其与电子输运的关系和测量方法。

With their size shrunk to nano scale, electronic devices have entered into the quantum regime. As an intrinsic characteristic of quantum systems, quantum entanglement is highly correlated with the behavior of quantum devices. Its quantification has been the main approach to predict critical behaviors such as quantum phase transition in materials and can be a key parameter for designing and understanding novel quantum devices. Recently, quantum entanglement of electrons in two-probe nano-devices has attracted much attention. Nevertheless, the complexity of the conventional method based on many-body density matrix increases exponentially with the system scale. It is then extremely difficult to handle the non-equilibrium many-body situation which is usually the case of devices in work. In this project, we will employ the non-equilibrium Green’s function method to transfer the many-body problem into a single-body one whose complexity is proportional to the system scale. In this way, we can extend the correlation matrix method for von Neumann entanglement entropy established in equilibrium states to non-equilibrium states. Currently, the method to evaluate entanglement entropy from the correlation matrix has been well established. The non-equilibrium Green’s function method has achieved great success on studying quantum transport in two-probe device systems by transferring many-body problems into single-body ones. Combining with the density functional theory, it has become the main candidate method of simulation and design for next-generation information quantum devices. Based on this, we will further study the quantum entanglement qualification of electrons, its correlation with the electron transport, and its measurement methods in nano devices of real materials.