Vortex confinement transitions in the modified Goldstone model
Vortex confinement transitions in the modified Goldstone model
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DOI：
10.1103/physrevresearch.2.013081
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发表时间：
2019-08
影响因子：
4.2
通讯作者：
Michikazu Kobayashi;Gergely FejHos;C. Chatterjee;M. Nitta
中科院分区：
文献类型：
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作者：
Michikazu Kobayashi;Gergely FejHos;C. Chatterjee;M. Nitta
修正的XY模型是XY模型的一个变体，扩展了半周期项，表现出丰富的相结构。由于Goldstone模型，也称为线性O（2）模型，可以作为XY模型的连续和正则模型得到，我们定义修改的Goldstone模型为修改的XY模型。我们构造了一个涡旋，一个孤子（畴壁），和一个分子的两个半量子化的涡旋连接的孤子作为该模型的正规解。然后我们通过泛函重整化群方法和全数值模拟研究了它在两个欧几里德维中的相结构。我们认为，场的依赖性的波函数重整化因子中起着至关重要的作用，在存在的不动点线描述的Berezinskiii-Kosterlitz-无（BKT）过渡，最终可以终止不仅在一个，但在两个端点的修改后的模型。这种结构证实了系统中可以发生BKT和Ising型的两步相变。我们比较我们的重整化群结果与完整的数值模拟，这也表明，相变显示出比预期更丰富的场景。
The modified XY model is a variation of the XY model extended by a half periodic term, exhibiting a rich phase structure. As the Goldstone model, also known as the linear O(2) model, can be obtained as a continuum and regular model for the XY model, we define the modified Goldstone model as that of the modified XY model. We construct a vortex, a soliton (domain wall), and a molecule of two half-quantized vortices connected by a soliton as regular solutions of this model. Then we investigate its phase structure in two Euclidean dimensions via the functional renormalization group formalism and full numerical simulations. We argue that the field dependence of the wave function renormalization factor plays a crucial role in the existence of the line of fixed points describing the Berezinskii-Kosterlitz-Thouless (BKT) transition, which can ultimately terminate not only at one but at two end points in the modified model. This structure confirms that a two-step phase transition of the BKT and Ising types can occur in the system. We compare our renormalization group results with full numerical simulations, which also reveal that the phase transitions show a richer scenario than expected.