Relationship between the wave function of a magnet and its static structure factor

Abstract

We state and prove two theorems about the ground state of magnetic systems described by very general Heisenberg-type models. The first theorem states that the relationship between the Hamiltonian and the ground-state correlators is invertible. The second theorem states that the relationship between the wave function and the correlators is also invertible. We discuss the implications of these theorems for neutron scattering. We propose, in particular, a variational approach to quantum magnets where a representation of the wave function (held, for instance, in a neural network or in the qubit register of a quantum processor) is optimised to fit experimental neutron-scattering data directly, without the involvement of a model Hamiltonian.