Numerical Analysis of Finite Dimensional Approximations in Finite Temperature DFT

TL;DR

This paper investigates the numerical approximation methods for finite temperature density functional theory, establishing convergence, error estimates, and supporting numerical experiments for ground state calculations.

Contribution

It introduces a rigorous framework for finite dimensional approximations in finite temperature DFT, including convergence proofs and optimal error bounds.

Findings

Finite dimensional approximations converge to the true ground states.

An optimal a priori error estimate is established.

Numerical experiments validate the theoretical results.

Abstract

In this paper, we study numerical approximations of the ground states in finite temperature density functional theory. We formulate the problem with respect to the density matrices and justify the convergence of the finite dimensional approximations. Moreover, we provide an optimal a priori error estimate under some mild assumptions and present some numerical experiments to support the theory.