论文标题
$ bkt $在古典和量子远程系统中的过渡
$BKT$ transitions in classical and quantum long-range systems
论文作者
论文摘要
在过去的几十年中，已经做出了相当大的努力，以了解古典和量子远程相互作用模型的关键特征。 Berezinskii-Kosterlitz-thouless（BKT）通用类别（如$ 2D $经典的$ XY $模型中）的情况非常复杂，对于短期相互作用而言，是重量级化组固定点的一行。在本文中，我们讨论了带有远距离耦合的$ 2D $ xy $型号的字段理论处理，我们将其与自一致的谐波近似的结果进行了比较。这些方法导致了丰富的相图，其中幂律BKT缩放率和自发对称性断裂出现在相同的（中间）延长相互作用的速率上。我们还讨论了带有幂律联轴器的$ 2D $ xy $型号的反派近似，提供了提示，在远程制度中，它无法再现正确的关键行为。然后将获得的结果应用于零温度下的远程量子XXZ自旋链。我们讨论了两个模型的相位图之间的关系，并给出了关于量子链的量表缩放量的预测，量子链的量表接近过渡。
In the past decades considerable efforts have been made in order to understand the critical features of both classical and quantum long-range interacting models. The case of the Berezinskii-Kosterlitz-Thouless (BKT) universality class, as in the $2d$ classical $XY$ model, is considerably complicated by the presence, for short-range interactions, of a line of renormalization group fixed points. In this paper we discuss a field theoretical treatment of the $2d$ $XY$ model with long-range couplings and we compare it with results from the self-consistent harmonic approximation. These methods lead to a rich phase diagram, where both power-law BKT scaling and spontaneous symmetry breaking appear for the same (intermediate) decay rates of long-range interactions. We also discuss the Villain approximation for the $2d$ $XY$ model with power-law couplings, providing hints that, in the long-range regime, it fails to reproduce the correct critical behavior. The obtained results are then applied to the long-range quantum XXZ spin chain at zero temperature. We discuss the relation between the phase diagrams of the two models and we give predictions about the scaling of the order parameter of the quantum chain close to the transition.
