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. In this research project, we aim to explore the potential of Physics Informed Neural Networks (PINNs) to approximate the ground-truth state FIM in predicting quantum phase transitions. We hypothesize that the PINNs will perform faster in predicting the ground-state FIM values compared to current approaches such as Monte-Carlo, Lanczos, and density matrix renormalization group (DMRG), which are much more computationally intensive.