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

TL;DR

This paper presents two theorems linking the ground-state wave function of magnetic systems to their static structure factor, with implications for neutron scattering analysis and quantum magnet modeling.

Contribution

It introduces novel theorems that connect ground states and correlators, enabling model-independent analysis of neutron scattering data and quantum wave function optimization.

Findings

Theorems establish unique ground state-correlator relationships.

Framework for neutron-based Hamiltonian learning.

Proposed variational approach for quantum magnet modeling.

Abstract

We state and prove two theorems about the ground state of magnetic systems described by very general Heisenberg-type models and discuss their implications for magnetic neutron scattering. The first theorem states that two models cannot have the same correlator without sharing the corresponding ground states. According to the second theorem, an $N$-qubit wave function cannot reproduce the correlators of a given system unless it represents a true ground state of that system. We discuss the implications for neutron scattering inverse problems. We argue that the first theorem provides a framework to understand neutron-based Hamiltonian learning. Furthermore, we propose a variational approach to quantum magnets based on the second theorem 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.