title: A Density Functional Theory View of Quantum Phase Transitions.
abstract: It is shown that there is a one-to-one map between the ground state wave function and the control parameter. Wu et al. [Phys. Rev. A2006, 74, 052335] introduced an analogue of the Density Functional Theory (DFT) density and showed that the "density" determines the "control parameter" (corresponding to the DFT "external potential"). We prove that any strictly monotonous function can be used to obtain a new density with a different control parameter (or DFT "external potential"), and the new density determines the new control parameter. Moreover, there is also a one-to-one map between the Rényi entropy of a given order and the control parameter. Therefore, the Rényi entropy can be used as a control parameter.
authors.affiliation: Department of Theoretical Physics, University of Debrecen, H-4010 Debrecen, Hungary.|Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain.
authors.forename: Á
authors.initials: Á
authors.lastname: Nagy
authors.affiliation: Departamento de Matemática Aplicada, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain.
authors.forename: M
authors.initials: M
authors.lastname: Calixto
authors.affiliation: Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain.|Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, Fuentenueva s/n, 18071 Granada, Spain.
authors.forename: E
authors.initials: E
authors.lastname: Romera