论文标题
二维变形Affleck-Kennedy-Lieb-Tasaki状态的有限尺寸缩放分析
Finite-size scaling analysis of two-dimensional deformed Affleck-Kennedy-Lieb-Tasaki states
论文作者
论文摘要
使用张量网络方法，我们执行有限尺寸的缩放分析，以研究参数诱导的二维变形Affleck-Kennedy-Lieb-Tasaki状态的相变。我们使用高阶张量重新归化组方法来评估矩和相关性。然后，通过折叠数据同时确定临界点和临界指数。或者，无量纲比率的交叉点用于确定临界点，并使用临界点处的缩放来确定临界指数。对于无序的AKLT阶段与铁磁有序相之间的过渡，我们证明了临界点和指数都可以准确确定。此外，指数的值确认AKLT-FM过渡属于2D ISING通用类别。我们还研究了从AKLT阶段到临界XY阶段的Berezinskii-Kosterlitz-无尽的过渡。在这种情况下，我们表明临界点可以通过相关比的交叉点找到。
Using tensor network methods, we perform finite-size scaling analysis to study the parameter-induced phase transitions of two-dimensional deformed Affleck-Kennedy-Lieb-Tasaki states. We use higher-order tensor renormalization group method to evaluate the moments and the correlations. Then, the critical point and critical exponents are determined simultaneously by collapsing the data. Alternatively, the crossing points of the dimensionless ratios are used to determine the critical point, and the scaling at the critical point is used to determine the critical exponents. For the transition between the disordered AKLT phase and the ferromagnetic ordered phase, we demonstrate that both the critical point and the exponents can be determined accurately. Furthermore, the values of the exponents confirm that the AKLT-FM transition belongs to the 2D Ising universality class. We also investigate the Berezinskii-Kosterlitz-Thouless transition from the AKLT phase to the critical XY phase. In this case we show that the critical point can be located by the crossing point of the correlation ratio.
