Numerical Simulation of Two-Dimensional Quantum XYX Model Based on Tensor Network Algorithm

The Tensor Network (TN) algorithm for strongly related electronic quantum lattice systems has become the uppermost algorithm for studying strongly related electronic quantum lattice systems in numerical computation. Focusing on the TN algorithm based on 2-D spin systems, this paper discusses the theoretical principles of the Projected Entangled Pair States (PEPS) algorithm and its implementation process. It also explores the infinite PEPS (iPEPS) algorithm for simulating the spin-1/2 infinite 2-D square lattice quantum XYX model. The critical phenomena of the two-dimensional XYX quantum system are analyzed from the perspectives of ground-state fidelity and order parameters, and the quantum critical point is identified. It is anticipated that with the further development of TN algorithms, the single-site fidelity theory of quantum phase transitions (QPTs) can be applied to various quantum many-body systems in condensed matter physics, thereby deepening our understanding of the extremely rich states of matter in the quantum world. Research indicates that quantum information theory provides a universal method for the study of QPTs, which can identify several ground-state fidelities and order parameters through the ground-state wave function of the system, several ground state fidelity and local order parameters can be identified to fully describe some quantum phase transition points, greatly enriching the traditional Landau theory of symmetry breaking QPTs.