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.

翻译：本文研究了有限温度密度泛函理论中基态的数值逼近。我们以密度矩阵形式建立问题，并证明了有限维逼近的收敛性。此外，在若干温和假设下给出了最优先验误差估计，并通过数值实验支持理论分析。