Exact time-dependent density functional theory for impurity models

TL;DR

This paper uses the density matrix renormalization group to construct the exact time-dependent exchange correlation potential in impurity models under transport voltage, revealing fundamental challenges in transport calculations with time-dependent density functional theory.

Contribution

It demonstrates the construction of the exact time-dependent exchange correlation potential for impurity models, highlighting the long-range nature and immediate build-up after voltage application.

Findings

Exchange correlation potential is infinitely long-ranged.

Potential builds up instantly after switching on voltage.

Highlights difficulties in transport calculations using TDDFT.

Abstract

We employ the density matrix renormalization group to construct the exact time-dependent exchange correlation potential for an impurity model with an applied transport voltage. Even for short-ranged interaction we find an infinitely long-ranged exchange correlation potential which is built up {instantly} after switching on the voltage. Our result demonstrates the fundamental difficulties of transport calculations based on time-dependent density functional theory. While formally the approach works, important information can be missing in the ground-state functionals and may be hidden in the usually unknown non-equilibrium functionals.