Machine learning of frustrated classical spin models (II): Kernel principal component analysis

被引：0
作者：
Ce Wang
Hui Zhai
机构：
[1] Tsinghua University,Institute for Advanced Study
[2] Collaborative Innovation Center of Quantum Matter,undefined
来源：
Frontiers of Physics | 2018年 / 13卷
关键词：
machine learning; classical ; model; kernel PCA; frustrated lattice;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this work, we apply a principal component analysis (PCA) method with a kernel trick to study the classification of phases and phase transitions in classical XY models of frustrated lattices. Compared to our previous work with the linear PCA method, the kernel PCA can capture nonlinear functions. In this case, the Z2 chiral order of the classical spins in these lattices is indeed a nonlinear function of the input spin configurations. In addition to the principal component revealed by the linear PCA, the kernel PCA can find two more principal components using the data generated by Monte Carlo simulation for various temperatures as the input. One of them is related to the strength of the U(1) order parameter, and the other directly manifests the chiral order parameter that characterizes the Z2 symmetry breaking. For a temperature-resolved study, the temperature dependence of the principal eigenvalue associated with the Z2 symmetry breaking clearly shows second-order phase transition behavior.
引用
收藏
相关论文
共 69 条
[1]  
Wang C.(2017)Machine learning of frustrated classical spin models (I): Principal component analysis Phys. Rev. B 96 14443-undefined
[2]  
Zhai H.(2016)Discovering phase transitions with unsupervised learning Phys. Rev. B 94 195105-undefined
[3]  
Wang L.(2017)Machine learning phases of matter Nat. Phys 13 431-undefined
[4]  
Carrasquilla J.(2017)Learning phase transitions by confusion Nat. Phys 13 435-undefined
[5]  
Melko R.G.(2016)Learning thermodyamics with Boltzmann machines Phys. Rev. B 94 165134-undefined
[6]  
van Nieuwenburg E. P. L.(2017)Unsupervised learning of phase transitions: From principal component analysis to variational autoencoders Phys. Rev. E 96 022140-undefined
[7]  
Liu Y. H.(2017)Kernel methods for interpretable machine learning of order parameters Phys. Rev. B 96 205146-undefined
[8]  
Huber S. D.(2017)Discovering phases, phase transitions, and crossovers through unsupervised machine learning: A critical examination Phys. Rev. E 95 062122-undefined
[9]  
Torlai G.(2018)Unsupervised machine learning account of magnetic transitions in the Hubbard model Phys. Rev. E 97 013306-undefined
[10]  
Melko R. G.(2017)Principal component analysis for fermionic critical points Phys. Rev. B 96 195138-undefined
1234567