Learning topological defects formation with neural networks in a quantum phase transition

被引:0
|
作者
Han-Qing Shi [1 ]
Hai-Qing Zhang [1 ,2 ]
机构
[1] Center for Gravitational Physics, Department of Space Science, Beihang University
[2] Peng Huanwu Collaborative Center for Research and Education, Beihang University
基金
中国国家自然科学基金;
关键词
D O I
暂无
中图分类号
O469 [凝聚态物理学]; TP183 [人工神经网络与计算];
学科分类号
070205 ; 081104 ; 0812 ; 0835 ; 1405 ;
摘要
Neural networks possess formidable representational power, rendering them invaluable in solving complex quantum many-body systems. While they excel at analyzing static solutions,nonequilibrium processes, including critical dynamics during a quantum phase transition, pose a greater challenge for neural networks. To address this, we utilize neural networks and machine learning algorithms to investigate time evolutions, universal statistics, and correlations of topological defects in a one-dimensional transverse-field quantum Ising model. Specifically, our analysis involves computing the energy of the system during a quantum phase transition following a linear quench of the transverse magnetic field strength. The excitation energies satisfy a power-law relation to the quench rate, indicating a proportional relationship between the excitation energy and the kink numbers. Moreover, we establish a universal power-law relationship between the first three cumulants of the kink numbers and the quench rate,indicating a binomial distribution of the kinks. Finally, the normalized kink-kink correlations are also investigated and it is found that the numerical values are consistent with the analytic formula.
引用
收藏
页码:70 / 78
页数:9
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