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

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Cited by in corpus (7)

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• A Snapshot of Time-Dependent Density-Functional Theory
• Density Functional Theory of the Hubbard-Holstein Model
• Time-resolved spectroscopy at surfaces and adsorbate dynamics: insights from a model-system approach
• Dissipation and spontaneous emission in quantum electrodynamical density functional theory based on optimized effective potential: A proof of concept study