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

作　　者：Han-Qing Shi Hai-Qing Zhang 

机构地区：[1]Center for Gravitational Physics,Department of Space Science,Beihang University,Beijing 100191,China [2]Peng Huanwu Collaborative Center for Research and Education,Beihang University,Beijing 100191,China

出　　处：《Communications in Theoretical Physics》2024年第5期68-76,共9页理论物理通讯（英文版）

基　　金：partially supported by the National Natural Science Foundation of China(Grants No.11875095 and 12175008).

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.

关 键 词：neural networks machine learning transverse-field quantum Ising model kibble-zurek mechanism 

分 类 号：O469[理学—凝聚态物理] TP183[理学—电子物理学]