论文标题
非省力aubry-andré模型中定位 - 迁移过渡的非平衡动力学
Nonequilibrium dynamics of the localization-delocalization transition in the non-Hermitian Aubry-André model
论文作者
论文摘要
在本文中，我们调查了具有周期性边界条件的非俄勒冈州奥布里·安德烈模型中定位跃迁的驱动动力学。根据准周期电位$λ$的强度，该模型经历了定位 - 偏置相变。我们发现，本地化长度$ξ$满足$ \ varepsilon $是距关键点的距离，而$ν= 1 $是独立于非Hermitian参数的通用关键指标。此外，从基态和第一个激发状态之间的能量差距的有限尺寸缩放中，我们将动态指数$ z $确定为$ z = 2 $。 $ n $ th th $ n $ n $ th $ s = 0.1197 $的逆参与率（IPR）的关键指数也被确定。通过将$ \ varepsilon $线性更改以越过关键点，我们发现驱动动力学可以由kibble-zurek缩放（kzs）描述。此外，我们表明具有相同指数集的KZ可以推广到激发态中的定位相变。
In this paper, we investigate the driven dynamics of the localization transition in the non-Hermitian Aubry-André model with the periodic boundary condition. Depending on the strength of the quasi-periodic potential $λ$, this model undergoes a localization-delocalization phase transition. We find that the localization length $ξ$ satisfies $ξ\sim \varepsilon^{-ν}$ with $\varepsilon$ being the distance from the critical point and $ν=1$ being a universal critical exponent independent of the non-Hermitian parameter. In addition, from the finite-size scaling of the energy gap between the ground state and the first excited state, we determine the dynamic exponent $z$ as $z=2$. The critical exponent of the inverse participation ratio (IPR) for the $n$th eigenstate is also determined as $s=0.1197$. By changing $\varepsilon$ linearly to cross the critical point, we find that the driven dynamics can be described by the Kibble-Zurek scaling (KZS). Moreover, we show that the KZS with the same set of the exponents can be generalized to the localization phase transitions in the excited states.
