论文标题
从随机矩阵理论中的动力量子相变
Dynamical quantum phase transitions from random matrix theory
论文作者
论文摘要
我们使用随机矩阵理论及其相关的平面极限概念来发现一种新型的动力学量子相变。我们研究了各向同性XY Heisenberg自旋链。为此，我们通过Loschmidt Echo探测其实时动力学。这导致研究了一个复杂的重量的随机矩阵集合，其分析需要我们发展的新技术考虑。我们获得了三个主要结果：1）我们确定的关键时间有三阶相变。 2）三阶相变持续远离热力学极限。 3）对于低于临界值的时间，热力学极限和有限链之间的差异随系统尺寸呈指数减小。所有这些结果都以丰富的方式取决于符合保真度的量子状态的旋转数量的均等。
We uncover a novel dynamical quantum phase transition, using random matrix theory and its associated notion of planar limit. We study it for the isotropic XY Heisenberg spin chain. For this, we probe its real-time dynamics through the Loschmidt echo. This leads to the study of a random matrix ensemble with a complex weight, whose analysis requires novel technical considerations, that we develop. We obtain three main results: 1) There is a third order phase transition at a rescaled critical time, that we determine. 2) The third order phase transition persists away from the thermodynamic limit. 3) For times below the critical value, the difference between the thermodynamic limit and a finite chain decreases exponentially with the system size. All these results depend in a rich manner on the parity of the number of flipped spins of the quantum state conforming the fidelity.
