Exploring The Phase Transition In The J₁-J₂ Antiferromagnetic Heisenberg Spin Chain By Machine Learning

Exploring quantum phase transition through order parameters is a traditional method?Recently,machine learning method has become a new tool to explore phase transition.In this paper,the phase transition of J₁-J₂ antiferromagnetic Heisenberg spin chain model is studied by using gaussian mixture model and convolutional neural network model.The research results show that:(1)the machine learning method can accurately find the first-order phase transition point of the J₁-J₂ antiferromagnetic Heisenberg spin chain model from the ground state without any prior knowledge,but cannot find the infinite-order phase transition point.From the first excited state,the first-order phase transition point and the infinite-order phase transition point can be found,which indirectly shows that the first excited state may contain more information than the ground state;(2)Supervised learning can Identify the phase transition points extracted by unsupervised learning and remove false phase transition points,which shows that useful information can be found from a large amount of data only by using machine learning methods,which can be used as an effective tool to identify phase transitions.The state vector and convolutional neural network intermediate layer output visualizations illustrate the reliability of machine learning algorithms.