Drude weights in one-dimensional systems with a single defect
Drude weights in one-dimensional systems with a single defect
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具有单一缺陷的一维系统中的德鲁德权重
DOI：
10.1103/physrevb.107.075141
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发表时间：
2023
影响因子：
3.7
通讯作者：
Watanabe Haruki
中科院分区：
文献类型：
--
作者：
Takasan Kazuaki;Oshikawa Masaki;Watanabe Haruki
量子系统的弹道输运可以用德鲁德重量来表征，德鲁德重量量化了系统在无限长时间尺度上对均匀电场的响应。Drude权经常根据Kohn公式进行讨论，该公式通过具有周期边界条件的有限尺寸系统的能量本征值对Aharonov-Bohm通量的导数给出Drude权。最近，Kohn公式被推广到非线性响应。然而，由Kohn公式确定的非线性Drude重量经常在热力学极限下发散。为了阐明这个问题，在这项工作中，我们研究了一个简单的例子，一个一维紧束缚模型中存在一个单一的缺陷在零温度。我们发现，它的线性和非线性Drude重量给出的Kohn公式（i）依赖于Aharonov-Bohm通量和（ii）发散成比例的系统大小的幂。我们认为，这个问题可以归因于不同的顺序的限制。根据Kohn公式的Drude重量（“Kohn-Drude重量”）指示有限尺寸系统对Aharonov-Bohm通量的绝热插入的响应。虽然它是有限尺寸系统的一个明确定义的物理量，但其热力学极限并不总是描述大体积的弹道输运。后者的特点应该是“散装德鲁德重量”的定义，首先采取热力学极限之前的零频率限制。虽然有时在线性响应中讨论了极限顺序的潜在问题，但在非线性Drude权重中放大了两个极限之间的差异。我们证明了低能量激发的重要性，这是排除在科恩-德鲁德重量，在正规化散装德鲁德重量。
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 nonlinear 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, which are excluded from the Kohn-Drude weight, in regularizing the bulk Drude weight.