论文标题
量子步行中拓扑相变的保真度易感性
Fidelity susceptibility near topological phase transitions in quantum walks
论文作者
论文摘要
在量子度量张量的背景下引入的保真度敏感性的概念是表征量子相变附近的关键性的重要数量。我们证明，对于狄拉克模型中的拓扑相变，只要动量空间被视为量子指标的多种流量，富达度的敏感性与曲率函数相吻合，曲率函数的整合使拓扑不变。因此，在拓扑相转变附近的曲率函数的量子临界性也描述了保真度敏感性的临界性，并且从曲率函数中提取的相关长度也给出了动量尺度，使富达易感性衰减。为了绘制忠诚度易感性的概况和临界性，我们转向量子步行，以模拟一维BDI和二维D级DIRAC模型，并证明了它们在捕获拓扑相变的关键指数和扩展定律方面的准确性。
The notion of fidelity susceptibility, introduced within the context of quantum metric tensor, has been an important quantity to characterize the criticality near quantum phase transitions. We demonstrate that for topological phase transitions in Dirac models, provided the momentum space is treated as the manifold of the quantum metric, the fidelity susceptibility coincides with the curvature function whose integration gives the topological invariant. Thus the quantum criticality of the curvature function near a topological phase transition also describes the criticality of the fidelity susceptibility, and the correlation length extracted from the curvature function also gives a momentum scale over which the fidelity susceptibility decays. To map out the profile and criticality of the fidelity susceptibility, we turn to quantum walks that simulate one-dimensional class BDI and two-dimensional class D Dirac models, and demonstrate their accuracy in capturing the critical exponents and scaling laws near topological phase transitions.
