Mapping the Hubbard model to self-consistent spin models: a quantum-embedded Jordan-Wigner transformation

This work introduces a quantum-embeded Jordan-Wigner transformation which preserves the ground-state properties of fermionic Hamiltonians via the resolution of the representability problem within a variational many-body ansatz. As an example, the multi-orbital Hubbard model is mapped to a self-consistent local quantum spin model, utilizing the exact evaluation of the generalized Gutzwiller-Baeryswil wave-function in d=infty. This transformation reveals the order parameter of the Mott transition as the in-plane magnetization of the local quantum spin model, and the associated Landau theory is derived. Furthermore, the resulting local quantum spin model is amenable to solution via a quantum computer, thus presenting a pragmatic hybrid quantum-classical algorithm for scrutinizing the multi-orbital Hubbard model in thermodynamic limit.