Hubbard Model in a Cavity for a Diatomic Molecule

Abstract

In this work, we investigated light–matter interactions using the Hubbard dimer as a minimal two-site model representing a diatomic molecule. To incorporate the light–matter coupling, we employed the well-established Pauli–Fierz (PF) Hamilto- nian, which is applicable across both weak and strong coupling regimes, whereas the Jaynes–Cummings model is restricted to the weak coupling limit. We systematically analyzed both the weak and strong coupling limits, including the convergence behavior of the block structure within the P–F Hamiltonian. The study encompassed the characterization of energy levels (polaritonic potential energy surfaces) as functions of key Hubbard parameters, along with an examination of charge fluctuations and the average photon number associated with each eigenstate, and their dependence on the light–matter coupling strength. Furthermore, we explored the time evolution of the system under various condi- tions to gain insight into its dynamical behavior. Finally, we extended our framework to a realistic molecular system, lithium hydride (LiH), and investigated its polaritonic potential energy surfaces within the same theoretical formalism.