Abstract
We present a density functional theory (DFT) for lattice models with local electron-electron (e-e) and electron-phonon (e-ph) interactions. Exchange-correlation potentials are derived via dynamical mean field theory for the infinite-dimensional Bethe lattice, and analytically for an isolated Hubbard-Holstein site. These potentials exhibit discontinuities as a function of the density, which depend on the relative strength of the e-e and e-ph interactions. By comparing to exact benchmarks, we show that the DFT formalism gives a good description of the linear conductance and real-time dynamics.
Highlights
The quantum theory of solids, almost a century old, is unquestionably a great success story: A vast number of material properties and phenomena have been explained, resulting in technological advances with transformative effects [1,2]
Exchange-correlation potentials constructed via dynamical mean field theory for a D = ∞ Bethe lattice and analytically for an isolated site give a new perspective on e-ph screening of the e-e interactions and its effect on the charge- and spin-Kondo regimes
In the HH model the phonon XC potential is zero. (ii) The electronic XC potential is discontinuous at half-filling density n = 1 for U > 0 and at n = 0, 2 for U < 0; for the Bethe lattice, the discontinuity appears above a nonzero value of |U |. (iii) For an infinite chain with a HH impurity, (TD)density functional theory (DFT) conductances evolve smoothly from the charge- to the spin-Kondo regime upon varying the e-ph coupling. (iv) TDDFT dynamics in a test system subject to interaction quenches or external fields compares well with exact numerics in an appreciable range of interaction strengths
Summary
As starting point for the DFT description, we consider the inhomogeneous HH Hamiltonian. Where vi is a local site-dependent electron potential, μ is the chemical potential, U is the e-e interaction strength, J is the hopping amplitude (set equal to 1, as the energy unit), and · · · denotes nearest neighbor sites. The site-dependent external phonon coordinates xi potential = The form of Hin Eq (1) allows us to address formal aspects of the (TD)DFT description and to use a homogeneous. It allows us to prove the Hohenberg-Kohn theorem for the HH model (see Appendix A), putting the DFT treatment on solid ground. To calculate the ground-state energy of the reference homogenous HH model, we perform the Lang-Firsov transformation H → H = eiSHe−iS [38], resulting in.
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