Hohenberg-Kohn theorems for interactions, spin and temperature

Abstract

We prove Hohenberg-Kohn theorems for several models of quantum mechanics. First, we show that the pair correlation function of any ground state contains the information of the interactions and of the external potentials. Then, in the presence of the Zeeman interaction, a strong constraint on external fields is derived for systems having the same ground state densities and magnetizations. Moreover, we provide a counterexample in a setting involving non-local potentials. Next, we prove that the density and the entropy of a ground state contain the information of both the imposed external potential and temperature. Eventually, we conclude that at positive temperature, Hohenberg-Kohn theorems generically hold.

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Cited by in corpus (11)

• The structure of the density-potential mapping. Part I: Standard density-functional theory
• Some properties of the potential-to-ground state map in quantum mechanics
• Kinetic energy functionals and the $N$-representability of the electron pair-density given by the classical map hyper-netted-chain (CHNC) method
• Unique Continuation for the Magnetic Schrödinger Equation
• Revisiting density-functional theory of the total current density
• v-representability and Hohenberg-Kohn theorem for non-interacting Schrödinger operators with distributional potentials in the one-dimensional torus
• Learning interactions between Rydberg atoms
• A rigorous formulation of Density Functional Theory for spinless fermions in one dimension
• Mixed state representability of entropy-density pairs
• v-Representability on a one-dimensional torus at elevated temperatures
• Perspective on Moreau-Yosida Regularization in Density-Functional Theory