Reciprocal Asymptotically Decoupled Hamiltonian for use in Arbitrary Cavity Quantum Electrodynamics Potentials

This work provides a novel and rigorously derived representation for quantum electrodynamics (QED) Hamiltonians that efficiently converges for arbitrarily strong coupling strengths and is naturally applicable to periodic systems. Until now, light-matter Hamiltonians have been designed for small, finite, molecular systems, and they struggle to cheaply simulate solid-state, periodic systems in a cavity. Additionally, the computational cost for calculating the eigenspectra using most existing Hamiltonians scales very poorly with increasing coupling strength. With the introduction of the Reciprocal Asymptotically Decoupled (RAD) Hamiltonian, this work mitigates both of these difficulties. By explicitly working in reciprocal space, this unique representation can accurately describe periodic systems inside an optical cavity with a much smaller electronic basis set than typical Hamiltonians, while requiring only a few Fock states to converge for arbitrarily strong coupling strengths. Additionally, this work contains numerical results for both localized and periodic models.