TDDFT and Strongly Correlated Systems: Insight From Numerical Studies

TL;DR

This paper explores the capabilities of Time Dependent Density Functional Theory (TDDFT) in modeling strongly correlated lattice systems out of equilibrium, using exact numerical methods to analyze and approximate the exchange-correlation potential.

Contribution

It introduces an adiabatic local density approximation for the 1D Hubbard model and compares it with exact results to improve understanding of approximate exchange-correlation potentials.

Findings

ALDA provides insights into xc potentials for the Hubbard model.

Exact v_xc can be reverse engineered from many-body time evolution.

Remarks on v-representability for 1D Hubbard model are discussed.

Abstract

We illustrate the scope of Time Dependent Density Functional Theory (TDDFT) for strongly correlated (lattice) models out of equilibrium. Using the exact many body time evolution, we reverse engineer the exact exchange correlation (xc) potential $v_{xc}$ for small Hubbard chains exposed to time-dependent fields. We introduce an adiabatic local density approximation (ALDA) to $v_{xc}$ for the 1D Hubbard model and compare it to exact results, to gain insight about approximate xc potentials. Finally, we provide some remarks on the v-representability for the 1D Hubbard model.