Exact factorization-based density functional theory of electron-phonon systems

Abstract

Density functional theory is generalized to incorporate electron-phonon coupling. A Kohn-Sham equation yielding the electronic density $n_U(\mathbf{r})$, a conditional probability density depending parametrically on the phonon normal mode amplitudes $U=\{U_{\mathbf{q}\lambda }\}$, is coupled to the nuclear Schrödinger equation of the exact factorization method. The phonon modes are defined from the harmonic expansion of the nuclear Schrödinger equation. A nonzero Berry curvature on nuclear configuration space affects the phonon modes, showing that the potential energy surface alone is generally not sufficient to define the phonons. An orbital-dependent functional approximation for the non\-adiabatic exchange-correlation energy reproduces the leading-order nonadiabatic electron-phonon-induced band structure renormalization in the Fröhlich model.

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• Towards high-throughput superconductor discovery via machine learning
• Energy, Momentum and Angular Momentum Transfer Between Electrons and Nuclei
• Many-body Green's function theory of electrons and nuclei beyond the Born-Oppenheimer approximation
• Fock space embedding theory for strongly correlated topological phases
• Exact factorization of the many-body Green's function theory of electrons and nuclei
• Quantifying errors of the electron-proton/muon correlation functionals through the Kohn-Sham inversion of a two-component model system
• Geometric energy transfer in two-component systems
• Quantum covariant derivative
• Electronic decoherence along a single nuclear trajectory
• On the diagonalization of quadratic Hamiltonians