Tensor Network For Quantum Phase Transiton Of One Demesional Potts Model In An Alternative Magnetic Field

The research on quantum phase transition for quantum many-body system has been a spotlight in the field of condensed matter physics due to its various critical phenomena at critical points. As to obtain the system's exact solution by an analytical way is quite difficult due to its complexity, so the numerical method provides an optional choice. With the development of the computer science and technology, which also improves the computing precision and speed, more and more algorithms are developed to simulate the systems. Among one of them is the tensor network which is based on matrix product state(MPS) theory. In this thesis, this kind of algorithm is applied to study the one dimensional q-state quantum Potts model in an alternative external transverse magnetic field. The result shows that the model has two phases when tuning the external field. One is ferromagnetic phase and the other is paramagnetic phase as the standard quantum Potts model. But the difference is that the model obtains a continueous phase transition in alternative external field when q?4 which is 2 for standard quantum Potts model. Besides this, the fidelity, universal order parameter and Von Nuemann entropy are also studied with the algorithm. The corresponding results are also support our conclusion. In the end, the author fits the central charge for the model with the data and get an error which is less than 1% compared with the theoretical value. This proves that the results are all reliable.