标题： 无序量子链的动态电导率 显示英文标题

标题： Dynamical conductivity of disordered quantum chains

摘要： 我们研究了具有无序的一维量子系统的输运性质。 我们通过使用切比雪夫矩阵乘积态（CheMPS）方法，数值计算了具有最近邻相互作用和随机化学势的费米链的电导率的频率依赖性。 作为基准，我们首先研究了非相互作用的情况。 与精确对角化和解析解的比较表明，CheMPS的结果在广泛的频率范围内是可靠的。 然后，我们计算了不同相互作用和无序强度下相互作用系统的动态电导谱。 在高频区域，电导率按幂律衰减，指数与相互作用有关。 这种行为定性上与玻色化场论的预测一致，尽管数值计算的指数显示与解析预期值存在偏差。 我们还计算了出现电导率峰的特征钉扎频率。 我们确认即使在相互作用的情况下，它也直接与局域化长度的倒数相关。 我们证明局域化长度随无序强度呈幂律变化，指数取决于相互作用，并发现与场论预测有良好的定量一致。 在低频区域，我们发现其行为与非相互作用系统$\omega^{2}(\ln\omega)^{2}$一致，无论是否存在相互作用。 我们讨论了我们的发现对冷原子气体实验的意义。 显示英文摘要

摘要： We study the transport properties of a one dimensional quantum system with disorder. We numerically compute the frequency dependence of the conductivity of a fermionic chain with nearest neighbor interaction and a random chemical potential by using the Chebyshev matrix product state (CheMPS) method. As a benchmark, we investigate the noninteracting case first. Comparison with exact diagonalization and analytical solutions demonstrates that the results of CheMPS are reliable over a wide range of frequencies. We then calculate the dynamical conductivity spectra of the interacting system for various values of the interaction and disorder strengths. In the high frequency regime, the conductivity decays as a power law, with an interaction dependent exponent. This behavior is qualitatively consistent with the bosonized field theory predictions, although the numerical evaluation of the exponent shows deviations from the analytically expected values. We also compute the characteristic pinning frequency at which a peak in the conductivity appears. We confirm that it is directly related to the inverse of the localization length, even in the interacting case. We demonstrate that the localization length follows a power law of the disorder strength with an exponent dependent on the interaction, and find good quantitative agreement with the field theory predictions. In the low frequency regime, we find a behavior consistent with the one of the noninteracting system $\omega^{2}(\ln\omega)^{2}$ independently of the interaction. We discuss the consequences of our finding for experiments in cold atomic gases.