Journal of Statistical Physics

, Volume 177, Issue 3, pp 415–437 | Cite as

Hohenberg–Kohn Theorems for Interactions, Spin and Temperature

  • Louis GarrigueEmail author


We prove Hohenberg–Kohn theorems for several models of quantum mechanics. First, we show that for possibly degenerate systems of several types of particles, the pair correlation functions of any ground state contain 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. Also, 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, in particular they hold in the classical case.


Mathematical physics Quantum physics Statistical physics Density functional theory Hohenberg–Kohn theorems 



I warmly thank Mathieu Lewin, my PhD advisor, for having supervized me during this work. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement MDFT No 725528), and from the Allocation Moniteur Normalien.


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Authors and Affiliations

  1. 1.CEREMADEUniversité Paris-Dauphine, PSL Research UniversityParisFrance

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