论文标题
无序量子自旋链的Fock空间上的概率传输
Probability transport on the Fock space of a disordered quantum spin chain
论文作者
论文摘要
在理解无序量子多体系统动态的广泛主题中，人们可以提出的最简单的问题之一是：给定初始状态，它如何在相关的fock空间图上及时演变，从而在相关的fock空间图上及时演变？我们的核心目的是对量子不足无序的量子状态和概率转运的时间演变的详细定量描述。我们在一个无序的量子自旋链的背景下进行了调查，该量子链构成了无序驱动的多体定位过渡。实时动力学/概率传输显示出具有丰富的现象学，在厄运和多体局部相之间有明显不同。例如，在两个阶段，在中间时间发现动力学是强烈的不均匀性，但是尽管它在长期以来都在长期存在均匀性的情况下，但在本地化阶段，动力学在本质上是任意长时间的，而动力学在本质上仍然是不均匀的。同样，我们表明，Fock空间图上适当定义的动力长度尺寸与局部自旋 - 自动相关直接相关，因此，在厄基因相中自动相关的（异常）衰减，并且在局部化相中缺乏它。
Within the broad theme of understanding the dynamics of disordered quantum many-body systems, one of the simplest questions one can ask is: given an initial state, how does it evolve in time on the associated Fock-space graph, in terms of the distribution of probabilities thereon? A detailed quantitative description of the temporal evolution of out-of-equilibrium disordered quantum states and probability transport on the Fock space, is our central aim here. We investigate it in the context of a disordered quantum spin chain which hosts a disorder-driven many-body localisation transition. Real-time dynamics/probability transport is shown to exhibit a rich phenomenology, which is markedly different between the ergodic and many-body localised phases. The dynamics is for example found to be strongly inhomogeneous at intermediate times in both phases, but while it gives way to homogeneity at long times in the ergodic phase, the dynamics remain inhomogeneous and multifractal in nature for arbitrarily long times in the localised phase. Similarly, we show that an appropriately defined dynamical lengthscale on the Fock-space graph is directly related to the local spin-autocorrelation, and as such sheds light on the (anomalous) decay of the autocorrelation in the ergodic phase, and lack of it in the localised phase.
