论文标题
长期Kitaev链中的拓扑量子相变和关键性
Topological quantum phase transitions and criticality in a longer-range Kitaev chain
论文作者
论文摘要
为了从理论上研究拓扑模型中的量子相变和关键性，我们研究了具有长距离耦合（有限的邻居数）以及真正的远距离耦合（无限邻居数）的Kitaev链。我们对动量空间进行了广泛的拓扑表征，以探索获得高阶绕组数并分析其在模型中稳定性的性质的可能性。观察到从偶数和奇数到odd绕组数的相变的发生，系统中的长度降低了。我们得出拓扑量子关键线，并研究它们以了解关键的行为。观察到高阶绕组数的抑制，模型中的较长范围降低。我们表明，这种现象背后的机制是由于与较高的绕组数量相关的拓扑量子临界线的叠加和消失。通过研究浆果连接，我们显示了临界线与相应的临界指数一起叠加时可能的不同行为。我们通过动量空间表征分析远程模型的行为。我们还为问题提供了精确的解决方案，并讨论了工作的实验方面。
In an attempt to theoretically investigate the quantum phase transition and criticality in topological models, we study Kitaev chain with longer-range couplings (finite number of neighbors) as well as truly long-range couplings (infinite number of neighbors). We carry out an extensive topological characterization of the momentum space to explore the possibility of obtaining higher order winding numbers and analyze the nature of their stability in the model. The occurrences of phase transitions from even-to-even and odd-to-odd winding numbers are observed with decreasing longer-rangeness in the system. We derive topological quantum critical lines and study them to understand the behavior of criticality. A suppression of higher order winding numbers is observed with decreasing longer-rangeness in the model. We show that the mechanism behind such phenomena is due to the superposition and vanishing of the topological quantum critical lines associated with the higher winding number. Through the study of Berry connection we show the possible different behaviors of critical lines when they undergo superposition along with the corresponding critical exponents. We analyze the behavior of the long-range models through the momentum space characterization. We also provide exact solution for the problem and discuss the experimental aspects of the work.
