Research on Quantum Phase Diagram of t-J Model Based on Machine Learning Tensor Network Algorithm

By introducing the concepts and methods of machine learning, the traditional tensor network algorithm is upgraded to the machine learning tensor network algorithm in order to obtain more accurate results in complex systems. Under the context of the virtual time evolution tensor network algorithm established in the graded projection entangled pair state (gPEPS) representation of the two-dimensional strongly correlated electron infinite fermion system based on machine learning, this paper mainly investigates the quantum phase diagram, quantum phase transition and quantum entanglement of the two-dimensional t-J model related to high temperature superconductivity through the ground state energy. The research results showed that the t-J model has a phase separation line between the Heisenberg antiferromagnetic state with no vacancies and the state rich in vacancies, with the upper critical point at Jc=0.95t and the lower critical point at Jc=3.45t. It was found that at J=0.4t, in addition to the potential long-range ferromagnetic state, four different phases were composed in the different doping uniform regions: one wasis the superconducting phase with coexistence of charge and spin density waves and px(py) wave symmetry, one wasis the mixed superconducting phase with d+s wave superconducting pairing and spin triplet px(py) wave superconducting symmetry in the antiferromagnetic background, one wasis the superconducting phase with extended s-wave symmetry, and the other one iswas the superconducting phase with px(py) wave symmetry in the ferromagnetic background.