Local Integrals of Motion from Neural Networks

Abstract: Neural network quantum states (NNQS) is a novel machine learning method, based on restricted Boltzmann machines, previously used to represent the wave function in many-body quantum mechanics. In this thesis, we use NNQS to instead find integrals of motion, i.e., operators, commuting with the Hamiltonian, describing a system. We also attempt to use this method to find the phase transition in systems exhibiting many-body localization. The neural network is shown to be highly successful in finding integrals of motion for the considered systems, while the outcome of finding the phase transition is less conclusive.