Quantum electrodynamical time-dependent density functional theory on a lattice

Abstract

We present a rigorous formulation of the time-dependent density functional theory for interacting lattice electrons strongly coupled to cavity photons. We start with an example of one particle on a Hubbard dimer coupled to a single photonic mode, which is equivalent to the single mode spin-boson model or the quantum Rabi model. For this system we prove that the electron-photon wave function is a unique functional of the electronic density and the expectation value of the photonic coordinate, provided the initial state and the density satisfy a set of well defined conditions. Then we generalize the formalism to many interacting electrons on a lattice coupled to multiple photonic modes and prove the general mapping theorem. We also show that for a system evolving from the ground state of a lattice Hamiltonian any density with a continuous second time derivative is locally $v$-representable.

9 pages, 1 figure

References in corpus (4)

• Quantum Electrodynamical Density-Functional Theory: Bridging Quantum Optics and Electronic-Structure Theory
• Generalized rotating-wave approximation for arbitrarily large coupling
• Accurate numerical solution to the finite-size Dicke model
• Global fixed point proof of time-dependent density-functional theory

Cited by in corpus (1)

• Existence, Uniqueness, and Construction of the Density-Potential Mapping in Time-Dependent Density-Functional Theory