Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud, 150-Urca, 22290-180, Rio de Janeiro, RJ, Brazil.
Phys Rev E. 2018 Jan;97(1-1):012107. doi: 10.1103/PhysRevE.97.012107.
Topological phase transitions constitute a new class of quantum critical phenomena. They cannot be described within the usual framework of the Landau theory since, in general, the different phases cannot be distinguished by an order parameter, neither can they be related to different symmetries. In most cases, however, one can identify a diverging length at these topological transitions. This allows us to describe them using a scaling approach and to introduce a set of critical exponents that characterize their universality class. Here we consider some relevant models of quantum topological transitions associated with well-defined critical exponents that are related by a quantum hyperscaling relation. We extend to these models a finite-size scaling approach based on techniques for calculating the Casimir force in electromagnetism. This procedure allows us to obtain universal Casimir amplitudes at their quantum critical points. Our results verify the validity of finite-size scaling in these systems and confirm the values of the critical exponents obtained previously.
拓扑相变构成了一类新的量子临界点现象。它们不能用朗道理论的通常框架来描述，因为一般来说，不同的相不能用序参量来区分，也不能与不同的对称性联系起来。然而，在大多数情况下，可以在这些拓扑相变中识别出一个发散的长度。这使得我们能够使用标度方法来描述它们，并引入一组临界指数来描述它们的普遍性类别。在这里，我们考虑了一些与量子拓扑相变相关的模型，这些模型与量子超尺度关系有关，具有明确的临界指数。我们将基于计算电磁学中卡西米尔力的技术的有限尺寸标度方法扩展到这些模型中。该方法允许我们在量子临界点获得通用的卡西米尔幅度。我们的结果验证了该系统中有限尺寸标度的有效性，并确认了之前获得的临界指数的值。
