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arXiv · 1408.6324

Quantum electrodynamical time-dependent density functional theory on a lattice

Mehdi Farzanehpour·I. V. Tokatly
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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.

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Mehdi Farzanehpour, I. V. Tokatly. 2014-08-27. Quantum electrodynamical time-dependent density functional theory on a lattice. https://doi.org/10.1103/physrevb.90.195149

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