PINNs for Ground State Determination and Fisher Information-Based Phase Transition Detection
By Claire, Avery
Quantum phases are states of matter which exist at near absolute zero temperatures, where quantum effects govern the system. The transition between phases is called a quantum phase transition (QFT) and is of interest particularly when the order parameter, a value that usually characterizes transitions, is not known. Instead, quantum and classical phase transitions can be detected through the use of the Fisher Information Metric (FIM) in various unsupervised learning tasks. This project uses Physics-Informed Neural Networks (PINNs) to approximate ground-state FIM values across different quantum models, including the Frustrated Ising (ISN400), FIL24, Hubbard, and XXZ. A novel loss formulation is introduced to incorporate batch normalization during training, addressing a key limitation in previous models such as ClassiFiM, which struggled with large log-odds due to cross-entropy loss scaling. Our study finds that with PINNs there is generally comparable accuracy and runtime to that of ClassiFIM, though further research is needed into the speedup that PINNs actually presents.