论文标题
Loschmidt回波和动态量子相变的理论中无序的费米系统
Theory of the Loschmidt echo and dynamical quantum phase transitions in disordered Fermi systems
论文作者
论文摘要
在这项工作中，我们在淬灭后，发展了Loschmidt回声和动力学相变的理论。在有限的系统中，loschmidt Echo在复杂的时间平面中显示零，取决于随机电位实现。值得注意的是，零在热力学极限中形成一个2D歧管，对于1D系统而言是非典型的，在急剧定义的关键时间越过真实轴。我们表明，这种动力学相变可以理解为洛斯基米特矩阵最小特征值的分布函数中的转变，并开发有限尺寸的缩放理论。与期望相反，无序系统中动态相变的概念与安德森本地化过渡的平衡脱钩。我们的结果突出了无序和非隔离的多个特里米奥系统中淬灭动态的明显质量差异。
In this work we develop the theory of the Loschmidt echo and dynamical phase transitions in non-interacting strongly disordered Fermi systems after a quench. In finite systems the Loschmidt echo displays zeros in the complex time plane that depend on the random potential realization. Remarkably, the zeros coalesce to form a 2D manifold in the thermodynamic limit, atypical for 1D systems, crossing the real axis at a sharply-defined critical time. We show that this dynamical phase transition can be understood as a transition in the distribution function of the smallest eigenvalue of the Loschmidt matrix, and develop a finite-size scaling theory. Contrary to expectations, the notion of dynamical phase transitions in disordered systems becomes decoupled from the equilibrium Anderson localization transition. Our results highlight the striking qualitative differences of quench dynamics in disordered and non-disordered many-fermion systems.
