Resolving the Berezinskii-Kosterlitz-Thouless transition in the two-dimensional XY model with tensor-network-based level spectroscopy
Resolving the Berezinskii-Kosterlitz-Thouless transition in the two-dimensional XY model with tensor-network-based level spectroscopy
复制标题
使用基于张量网络的能级谱解决二维 XY 模型中的 Berezinskii-Kosterlitz-Thouless 转变
DOI：
10.1103/physrevb.104.165132
复制
发表时间：
2021
影响因子：
3.7
通讯作者：
Oshikawa Masaki
中科院分区：
文献类型：
--
作者：
Ueda Atsushi;Oshikawa Masaki
结合张量网络重整化（TNR）和基于保形场理论有限尺度的能级光谱方法，重新研究了经典XY模型的Berezinskii-Kosterlitz-Thouless跃迁。通过系统地分析各种中等大小的系统的传递矩阵谱，我们确定了除去对数修正的临界点，这些系统可以用有限的键维精确处理。这比以前的研究（包括那些利用TNR的研究）提高了一个数量级的准确性。我们的分析还基于数值数据给出了著名的Kosterlitz重整化群流的可视化。
Berezinskii-Kosterlitz-Thouless transition of the classical XY model is reinvestigated, combining the tensor network renormalization (TNR) and the level spectroscopy method based on the finite-size scaling of the conformal field theory. By systematically analyzing the spectrum of the transfer matrix of the systems of various moderate sizes, which can be accurately handled with a finite bond dimension, we determine the critical point removing the logarithmic corrections. This improves the accuracy by an order of magnitude over previous studies including those utilizing TNR. Our analysis also gives a visualization of the celebrated Kosterlitz renormalization group flow based on the numerical data.