This project explores the application of machine learning techniques in addressing physics problems, particularly in the realm of many-body systems. We focus on investigating quantum phase transitions, with a specific emphasis on topological phase transitions, which challenge traditional Landau classification due to the absence of a definitive order parameter.
We analyze the Kitaev Ladder model as a case study for quantum topological phase transitions. Our research demonstrates that the structural and magnetic properties of the Kitaev ladder network provide essential insights for identifying phases and delineating phase transition boundaries.
We also examine the four distinct phases of the Extended Bose-Hubbard model. The machine learning model is trained using Schmidt coefficients derived from the tensor network, yielding favorable results in identifying phase transitions.
The data necessary for machine learning was generated using the infinite Time Evolving Block Decimation (iTEBD) algorithm. This algorithm derives the ground state wave function of the target system through tensor networks, effectively mapping the Hamiltonians onto a tensor chain.
- Supervised Learning: We trained the model using the system's magnetization data for the Kitaev ladder model, which effectively pinpointed phase transition points and boundaries with a reasonable degree of accuracy.
- Unsupervised Learning: We applied anomaly detection techniques to identify the regions and boundaries of each phase, demonstrating the effectiveness of unsupervised learning in this context.
The analyses conducted on both models indicate that machine learning can effectively identify phase transition points and boundaries. The findings suggest that both supervised and unsupervised learning techniques are valuable tools for investigating quantum phase transitions.