Quantum simulation methods based on density-functional theory are currently deemed unfit to cope with atomic heat transport within the Green-Kubo formalism, because quantum-mechanical energy densities and currents are inherently ill-defined at the at
omic scale. We show that, while this difficulty would also affect classical simulations, thermal conductivity is indeed insensitive to such ill-definedness by virtue of a sort of gauge invariance resulting from energy extensivity and conservation. Based on these findings, we derive an expression for the adiabatic energy flux from density-functional theory, which allows heat transport to be simulated using ab-initio equilibrium molecular dynamics. Our methodology is demonstrated by comparing its predictions with those of classical equilibrium and ab-initio non-equilibrium (Muller-Plathe) simulations for a liquid-Argon model, and finally applied to heavy water at ambient conditions.
We introduce a new implementation of time-dependent density-functional theory which allows the emph{entire} spectrum of a molecule or extended system to be computed with a numerical effort comparable to that of a emph{single} standard ground-state ca
lculation. This method is particularly well suited for large systems and/or large basis sets, such as plane waves or real-space grids. By using a super-operator formulation of linearized time-dependent density-functional theory, we first represent the dynamical polarizability of an interacting-electron system as an off-diagonal matrix element of the resolvent of the Liouvillian super-operator. One-electron operators and density matrices are treated using a representation borrowed from time-independent density-functional perturbation theory, which permits to avoid the calculation of unoccupied Kohn-Sham orbitals. The resolvent of the Liouvillian is evaluated through a newly developed algorithm based on the non-symmetric Lanczos method. Each step of the Lanczos recursion essentially requires twice as many operations as a single step of the iterative diagonalization of the unperturbed Kohn-Sham Hamiltonian. Suitable extrapolation of the Lanczos coefficients allows for a dramatic reduction of the number of Lanczos steps necessary to obtain well converged spectra, bringing such number down to hundreds (or a few thousands, at worst) in typical plane-wave pseudopotential applications. The resulting numerical workload is only a few times larger than that needed by a ground-state Kohn-Sham calculation for a same system. Our method is demonstrated with the calculation of the spectra of benzene, C$_{60}$ fullerene, and of chlorofyll a.
