Learning quantum structures in compact localized eigenstates

Abstract

We study the emergence of structures that result from filling the compact localized states of the sawtooth and kagome lattices with interacting bosons. The ansatz for the many-body wave function is derived from the 'energy' of the restricted Boltzmann machine, and the network weights that parametrize the wave function are computed, or learned, from the minimization of the Monte-Carlo estimate of the ground-state energy. The results demonstrate that the emergence of the overall structure in interacting many-body systems is representable and optimizable by standard machine learning techniques with high fidelity, i.e. the residual errors are comparable to those made in estimating the ground-state energy. The local details of the emergent structures are, however, optimizable with a lower reliability.