Static and Time Dependent Density Functional Theory with Internal Degrees of Freedom: Merits and Limitations Demonstrated for the Potts Model

TL;DR

This paper extends density-functional theory to lattice gases with internal degrees of freedom, tests its accuracy on the Potts model, and discusses its limitations through comparisons with Monte Carlo simulations.

Contribution

It introduces an extension of DFT for systems with internal degrees of freedom and evaluates its effectiveness and limitations using the Potts model.

Findings

Excellent agreement with Monte Carlo simulations.

Identified key limitations of time-dependent DFT.

Validated the exact functional approach for the Potts model.

Abstract

We present an extension of the density-functional theory (DFT) formalism for lattice gases to systems with internal degrees of freedom. In order to test approximations commonly used in DFT approaches, we investigate the statics and dynamics of occupation (density) profiles in the one-dimensional Potts model. In particular, by taking the exact functional for this model we can directly evaluate the quality of the local equilibrium approximation used in time-dependent density-functional theory (TDFT). Excellent agreement is found in comparison with Monte Carlo simulations. Finally, principal limitations of TDFT are demonstrated.