Hunting for Hamiltonians: A Computational Approach to Learning Quantum Models

The machine learning community has been widely successful in developing computational methods for learning models, i.e., probability distributions, from data sets. We present a novel numerical method, similar in spirit to machine learning techniques, for learning quantum models, i.e., Hamiltonians, from wave functions. The method receives as input a target wave function and produces as output a space of Hamiltonians with the target wave function as an energy eigenstate. We demonstrate that our method is able to discover multi-dimensional spaces of Hamiltonians with ground states exactly identical to the ground states of known model Hamiltonians, such as the Kitaev chain, the XX chain, the Heisenberg chain, and the Majumdar-Ghosh model. Using this method, we also find a large space of Hamiltonians with a new type of antiferromagnetic ground state, exhibiting triplet dimer ordering, which has not been previously observed in other models. Our results indicate that our new computational approach can systematically discover new Hamiltonians, and thereby potentially new materials, with exactly specified ground state properties.