论文标题
具有单一缺陷的一维系统中的drude重量
Drude weights in one-dimensional systems with a single defect
论文作者
论文摘要
量子系统的弹道传输可以以磨碎的重量为特征，这量化了系统对无限长时间尺寸中均匀电场的响应。通常会根据Kohn Formula来讨论DRUDE的重量，该公式通过有限大小的系统的能量特征值的衍生物具有周期性边界条件，从而给出了DRUDE的重量。最近，Kohn公式概括为非线性响应。然而，由科恩公式确定的非线性磨光重量通常在热力学极限下发散。为了阐明问题，在这项工作中，我们研究了一个在零温度下单个缺陷的情况下的一维紧密结合模型的简单示例。我们发现，Kohn公式（i）给出的线性和非线性的Drude重量取决于Aharonov-Bohm通量，并且（ii）与系统大小的幂成立分歧。我们认为问题可以归因于不同的限制顺序。根据Kohn Formula（``Kohn-drude Toge''）的DRUDE重量表明有限大小的系统对Aharonov-Bohm通量的绝热插入的响应。虽然它是有限尺寸系统的明确定义的物理量，但其热力学极限并不总是描述整体的弹道传输。后者的特征应以``大量的drude重量''的特征，而在零频率限制之前先采取热力学极限来定义。虽然有时在线性响应中讨论了限制顺序的潜在问题，但在非线性drude权重中两种限制之间的差异被放大。我们证明了$ o（1/l）$的低能激发的重要性，这些激发被排除在kohn-drude重量之外，在正规化散装的drude重量方面的重要性。
Ballistic transport of a quantum system can be characterized by Drude weight, which quantifies the response of the system to a uniform electric field in the infinitely long timescale. The Drude weight is often discussed in terms of the Kohn formula, which gives the Drude weight by the derivative of the energy eigenvalue of a finite-size system with the periodic boundary condition in terms of the Aharonov-Bohm flux. Recently, the Kohn formula is generalized to nonlinear responses. However, the nonlinear Drude weight determined by the Kohn formula often diverges in the thermodynamic limit. In order to elucidate the issue, in this work we examine a simple example of a one-dimensional tight-binding model in the presence of a single defect at zero temperature. We find that its linear and non-linear Drude weights given by the Kohn formula (i) depend on the Aharonov-Bohm flux and (ii) diverge proportionally to a power of the system size. We argue that the problem can be attributed to different order of limits. The Drude weight according to the Kohn formula (``Kohn--Drude weight'') indicates the response of a finite-size system to an adiabatic insertion of the Aharonov-Bohm flux. While it is a well-defined physical quantity for a finite-size system, its thermodynamic limit does not always describe the ballistic transport of the bulk. The latter should be rather characterized by a ``bulk Drude weight'' defined by taking the thermodynamic limit first before the zero-frequency limit. While the potential issue of the order of limits has been sometimes discussed within the linear response, the discrepancy between the two limits is amplified in nonlinear Drude weights. We demonstrate the importance of the low-energy excitations of $O(1/L)$, which are excluded from the Kohn--Drude weight, in regularizing the bulk Drude weight.
