Relationship between the ground-state 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.

One-to-one correspondence between thermal structure factors and coupling constants of general bilinear Hamiltonians

“…The present Letter follows a recent work by J. Quintanilla 5 , which establishes a theorem valid for a general class of bilinear quantum spin Hamiltonians, Ĥ = i,j,α,β…”

“…Appendix A). The proof follows in a similar vein to the zerotemperature one by Quintanilla 5 , but the Rayleigh-Ritz variational principle is replaced by the Gibbs-Bogoliubov inequality 2,22 for the Helmholtz free energy. Let a system described by a Hamiltonian Ĥ be in contact with a thermal bath at temperature T .…”

One-to-one correspondence between thermal structure factors and coupling constants of general bilinear Hamiltonians

“…The present Letter follows a recent work by Quintanilla [5], which establishes a theorem valid for a general class of bilinear quantum spin Hamiltonians,…”

“…In addition to the aforementioned theorem on the bijection between the exchange constants J α,β i, j and the zero-temperature spin-spin correlators ρ α,β i, j (T = 0), Quintanilla also proved [5] a second theorem that establishes a one-to-one relation between ρ α,β i, j (T = 0) and the ground state wave function | 0 . This Letter will focus mainly on the first theorem, given its potential relevance within the context of the Hamiltonian learning problem for both the study of complex quantum condensed-matter systems and the verification of quantum technologies (cf.…”

“…The theorem proven by Quintanilla [5] for this class of bilinear spin Hamiltonians asserts that there exists a one-to-one correspondence between the exchange constants * joaquin.fernandez-rossier@inl.int J α,β i, j and the zero-temperature correlators…”