Abstract
For two-dimensional XYX quantum model, iPEPS algorithm can select randomly initial state evolution, and get two degenerate symmetric broken ground state wave functions. In the quantum model, not only bifurcation behavior of ground state fidelity can be used, but bifurcation behavior of reduced density matrix fidelity can also be used to determine the phase transition point and its type caused by spontaneous broken symmetry of quantum of the system. Therefore, spontaneous symmetry breaking based on fidelity bifurcation can determine quantum phase transition one quantum system had gone through. This nature provides a method to further study quantum critical phenomena in quantum multibody system
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