论文标题
在复杂的sachdev-ye-kitaev模型中运输的接近平衡方法
Near-Equilibrium Approach to Transport in Complex Sachdev-Ye-Kitaev Models
论文作者
论文摘要
我们通过直接解决稳态绿色的功能，该功能在其平衡值周围的小扰动方面直接求解了稳态绿色的功能，从而研究了一维复合物sachdev-ye-kitaev链的非平衡动力学。该模型表现出奇怪的金属行为，没有准颗粒，并具有能量和电荷的扩散传播。我们通过施加均匀的温度和化学势梯度来探索该系统的热电运输特性。然后，我们将保守的电荷及其相关电流扩展到这些梯度中的领先顺序，我们可以通过数值和分析的不同参数制度对其进行计算。这使我们能够提取运输系数的全温度和化学势依赖性。特别是，我们发现扩散率在各种范围内采用了一种简单的形式，并导致了简化的爱因斯坦关系。在低温下，我们还为Wiedemann-Franz比率恢复了先前已知的结果。此外，我们通过表明在所有温度下的混乱繁殖速率上都受到的扩散率特征值，建立了扩散与量子混乱之间的关系。我们的工作展示了在强烈相互作用的量子系统中对传输特性进行分析触及计算的重要例子，并揭示了一种更通用的方法来解决强烈耦合的传输。
We study the non-equilibrium dynamics of a one-dimensional complex Sachdev-Ye-Kitaev chain by directly solving for the steady state Green's functions in terms of small perturbations around their equilibrium values. The model exhibits strange metal behavior without quasiparticles and features diffusive propagation of both energy and charge. We explore the thermoelectric transport properties of this system by imposing uniform temperature and chemical potential gradients. We then expand the conserved charges and their associated currents to leading order in these gradients, which we can compute numerically and analytically for different parameter regimes. This allows us to extract the full temperature and chemical potential dependence of the transport coefficients. In particular, we uncover that the diffusivity matrix takes on a simple form in various limits and leads to simplified Einstein relations. At low temperatures, we also recover a previously known result for the Wiedemann-Franz ratio. Furthermore, we establish a relationship between diffusion and quantum chaos by showing that the diffusivity eigenvalues are upper bounded by the chaos propagation rate at all temperatures. Our work showcases an important example of an analytically tractable calculation of transport properties in a strongly interacting quantum system and reveals a more general purpose method for addressing strongly coupled transport.
